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Recording properties of a concentric needle electrode for electromyography as measured in an electrolytic… Sutter, Martin 1981

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RECORDING PROPERTIES OF A CONCENTRIC NEEDLE ELECTRODE FOR ELECTROMYOGRAPHY AS MEASURED IN AN ELECTROLYTIC TANK MODEL by MARTIN SUTTER Dip].. E l . - I n g . ETH, Swiss F e d e r a l I n s t i t u t e o f Technology Z f t r i c h , S w i t z e r l a n d , 1977 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE.REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE i n THE FACULTY OF GRADUATE STUDIES (Department o f E l e c t r i c a l E n g i n e e r i n g ) We a c c e p t t h i s t h e s i s as c o n f o r m i n g t o t h e r e q u i r e d s t a n d a r d THE UNIVERSITY OF BRITISH COLUMBIA J u l y 1981 © M a r t i n S u t t e r , 1931 In p r e s e n t i n g t h i s t h e s i s i n p a r t i a l f u l f i l m e n t of the requirements f o r an advanced degree a t the U n i v e r s i t y o f B r i t i s h Columbia, I agree t h a t the L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r r e f e r e n c e and study. I f u r t h e r agree t h a t p e r m i s s i o n f o r e x t e n s i v e copying of t h i s t h e s i s f o r s c h o l a r l y purposes may be granted by the head of my department or by h i s o r her r e p r e s e n t a t i v e s . I t i s understood t h a t c o p y i n g or p u b l i c a t i o n o f t h i s t h e s i s f o r f i n a n c i a l gain s h a l l not be allowed without my w r i t t e n p e r m i s s i o n . Department of The U n i v e r s i t y of B r i t i s h Columbia 2075 Wesbrook P l a c e Vancouver, Canada V6T 1W5 DE-6 (2/79) i i ABSTRACT The w i d e l y used c o n c e n t r i c n e e d l e e l e c t r o d e produces electromyograms t h a t do not e x a c t l y c o r r e s p o n d t o th e t r u e s i g n a l i n t h e muscle. The p r e s e n c e o f t h e e l e c t r o d e i n d u c e s d i s t o r t i o n s o f t h e o r i g i n a l f i e l d d i s t r i b u t i o n i n t h e muscle, and th e c a n n u l a does not a c t as a p e r f e c t r e f e r e n c e e l e c t r o d e o f z e r o v o l t a g e . In o r d e r t o a s s e s s the s i g n a l d i s t o r t i n g p r o p e r t i e s , which have n o t been n u m e r i c a l l y e s t a b l i s h e d , an experimental- i n v e s t i g a t i o n was c a r r i e d o u t . A d i p o l e g e n e r a t o r i n an e l e c t r o l y t i c tank was employed t o model a s i n g l e muscle f i b e r as w e l l as a motor u n i t e q u i v a l e n t . The p o t e n t i a l f i e l d was map-ped w i t h a p o i n t - s h a p e d e l e c t r o d e so t h a t t h e " t r u e " f i e l d d i s t r i b u t i o n as a b a s i s f o r comparisons was e s t a b l i s h e d . Three s u b - a s s e m b l i e s and a complete model c o n c e n t r i c n e e d l e e l e c t r o d e were s e p a r a t e l y a v a i l a b l e f o r measurements. The f i e l d d i s t o r t i n g p r o p e r t i e s o f t h e c o r e , t h e i n s u l a t o r s u r r o u n d i n g t h e core and the c a n n u l a , were e x p e r i m e n t a l l y q u a n t i f i e d . The c a n n u l a p o t e n t i a l was d etermined as a f u n c t i o n o f t h e i n s e r t i o n depth and as a f u n c t i o n of t h e s p a t i a l arrangement o f a nearby s i n g l e f i b e r o r a motor u n i t . The o v e r a l l d i s -t o r t i o n s i n t r o d u c e d by the c o n c e n t r i c n e e d l e e l e c t r o d e were measured f o r both s i n g l e f i b e r and motor u n i t p o t e n t i a l s . F i n a l l y , w i t h the knowledge g a i n e d i n t h e i n v e s t i g a t i o n , a new c o n c e n t r i c n e e d l e e l e c t r o d e was d e s i g n e d and t e s t e d which e v i n c e d s u b s t a n t i a l improvements i n i t s r e c o r d i n g f i d e l i t y compared t o t h e c o n v e n t i o n a l d e s i g n . i i i TABLE OF CONTENTS Page ABSTRACT . i i LIST OF FIGURES . . . v i LIST OF SYMBOLS v i i i ACKNOWLEDGEMENT ix I. INTRODUCTION 1 1.1 The Muscle • • 2 1.2 The S i n g l e F i b e r Model 4 1.3 L i m i t a t i o n s o f t h e S i n g l e F i b e r L a b o r a t o r y Model . . . . . . 8 1.4 EMG E l e c t r o d e s . . . . . 10 1.5 The C o n c e n t r i c Needle E l e c t r o d e 13 1*6 The Problem o f CNEMG Measurement 15 I I . EXPERIMENTAL APPARATUS 18 2 .1 The Muscle F i b e r A n a l o g 19 2.2 The E l e c t r o l y t i c Tank 20 2*3 V e r i f i c a t i o n o f t h e Tank P r o p e r t i e s 25 2.4 G e o m e t r i c a l and F h y s i c a l S i m i l a r i t y . . . . . . . 25 The M e t a l - T i s s u e I n t e r f a c e . 27 S h u n t i n g o f Volume Conductor C u r r e n t s . . . . . . . . . . 28 W a l l E f f e c t 29 P o t e n t i a l A v e r a g i n g . . . . 30 V e r i f i c a t i o n Measurements . . . . . . . . . . . . . . . . 30 2.5 E l e c t r o d e s . . 34 The P o i n t E l e c t r o d e 36 The P o i n t E l e c t r o d e Surrounded by an " I n s u l a t i n g W a l l " . . 37 Development o f t h e CN E l e c t r o d e Model . . . . . 38 'Core' 39 'Core & I n s u l a t i o n " . . . . . . . . . . . . . . 40 Complete E l e c t r o d e . . . . . . . . . . . . . 41 The R e f e r e n c e E l e c t r o d e . 42 Treatment o f t h e L e a d i n g - o f f S u r f a c e • 43 iv Page 2.6 E l e c t r i c a l Apparatus 44 D i p o l e Source G e n e r a t o r . . . . . . . . . . . 44 The C u r r e n t Source . . . . . . 45 The Measuring Set-up . . . . . . . . . . . 46 The A m p l i f i e r 49 M i s c e l l a n e o u s . . . . . . . . 50 I I I . RESULTS & DISCUSSION 52 3.1 G e n e r a l Remarks 53 R e c o r d i n g D i s t a n c e r . . . . . . . . 53 A x i a l D i s t a n c e z . . . . . . . . . . . . . . 54 V e r t i c a l D i s t a n c e y 54 I n s e r t i o n Depth d 54 R e l a t i v e P o s i t i o n o f E l e c t r o d e and F i b e r s . . . . . . . . 55 PTPA . . . . . . . . . . . 56 PTPD 56 SD . 56 Key Symbols 56 3.2 The W a l l E f f e c t . . 57 3.3 The 'Core* Alone . • 57 3.4 The 'Core & I n s u l a t i o n ' Assembly . . . . . . . . 58 3.5 The Complete C o n c e n t r i c Needle E l e c t r o d e . . . . 61 3.6 S i n g l e F i b e r P o t e n t i a l Measurements . . . . . . . . . . . . 63 Peak-to-peak Amplitude . . . . . . . . 63 Peak-to-peak D u r a t i o n . . . . . . . . . . . . . . . . . . 65 Spike D u r a t i o n 70 3.7 E f f e c t o f D i f f e r e n t Cannula I n s e r t i o n Depths • • 70 3.8 The Motor U n i t Model 78 3.9 Motor U n i t P o t e n t i a l Measurements . . . . . . . 81 Cannula P o t e n t i a l . . . . . . . . . . . . . 81 Peak-to-peak Amplitude . . . . . . . 83 Peak-to-peak D u r a t i o n . . . . . . . . . . • . . . . • • . 83 Spike D u r a t i o n • • • 85 3.10 S p e c i a l E l e c t r o d e D e s i g n 87 Cannula P o t e n t i a l . . . . . . . . . . 89 Peak-to-peak Amplitude . . . . . . . . . . . . . . . . . 91 Peak-to-peak D u r a t i o n . . . . . . . . . . . . . . . . . . 97 Spike D u r a t i o n 97 V Page IV. CONCLUSIONS AND RECOMMENDATIONS . 1 0 4 4.1 C o n c l u s i o n s 105 F i e l d D i s t o r t i o n s 105 O v e r a l l D i s t o r t i o n s . . . . . . . . . . . 107 Cannula P o t e n t i a l 108 E l e c t r o d e Improvements 109 Summary 110 4.2 Recommendations . . . . . . . . . . . 110 BIBLIOGRAPHY . . . . . . 113 APPENDIX 118 v i L I S T OF FIGURES Page 1.1 The A c t i o n P o t e n t i a l . . . . . . . . . . 3 1.2 The S i n g l e F i b e r D i p o l e Concept 5 1.3 The P o t e n t i a l D i s t r i b u t i o n • • 6 1.4 E x t r a c e l l u l a r A c t i o n P o t e n t i a l s . . . . . . . . . . 7 1.5 A c t i o n P o t e n t i a l Nomenclature . . . . . . . . . 8 1.6 The C o n c e n t r i c Needle E l e c t r o d e . . . . . . . . . . 13 1.7 The DISA 13K53 CN E l e c t r o d e 14 2.1 The D i p o l e Model 20 2.2 The E l e c t r o l y t i c Tank Nomenclature . . . . . . . . . . 22 2*3 The F i b e r Frame ' 24 2.4 Computed and Measured I s o p o t e n t i a l L i n e s . . . . 26 2.5 The M e t a l - T i s s u e I n t e r f a c e . . . . . . 28 2.6 S h u n t i n g , W a l l E f f e c t and A v e r a g i n g 32 2.7 The E l e c t r o d e H o l d e r 35 2.8 The Complete P o s i t i o n i n g Assembly . . . 36 2.9 The P o i n t E l e c t r o d e 37 2.10 The 'Wall E f f e c t E l e c t r o d e ' . 38 2.11 The Core 40 2.12 Core & I n s u l a t i o n ; Complete E l e c t r o d e . . . . . . 41 2.13 The R e f e r e n c e E l e c t r o d e 43 2.14 Equ i v a l e n t . C i r c u i t of E l e c t r o l y t e , E l e c t r o d e and A m p l i f i e r . . . . 47 2.15 The E l e c t r i c a l A pparatus 50 3.1 Nomenclature o f t h e R e l a t i v e E l e c t r o d e P o s i t i o n . . . . 53 3.2 F r o n t and Back F i b e r s ; I n s e r t i o n Depth . . . . . . . . . . . . . 55 3.3 PTPA v s . r, 'Core'; F r o n t SFP . . . 59 3.4 PTPA v s . r , ' C o r e & I n s u l a t i o n " ; F r o n t SFP 60 3.5 R e l a t i v e PTPA v s . r , 'Core', 'Core & I n s u l a t i o n ' ; F r o n t SFP . . . 62 3.6 R e l a t i v e PTPA v s . r , Complete CNE; F r o n t SFP 64 3.7 R e l a t i v e PTPA v s . r , Complete CNE; F r o n t and Back SFP 66 3.8 PTPD v s . r , 'Core', 'Core & I n s u l a t i o n ' , Complete CNE; F r o n t SFP . 67 3.9 PTPD v s . r , Complete CNE; F r o n t and Back SFP . . . . . 69 v i i Page 3.10 SD v s . r , 'Core', 'Core & I n s u l a t i o n ' , Complete CNE; F r o n t SFP . . 71 3 .11 SD v s . r , Complete CNE; F r o n t and Back SFP 72 3 .12 Cannula PTPA v s . r , D i f f e r e n t I n s e r t i o n Depths; F r o n t SFP (y = 0 ) . 74 3 .13 Cannula PTPA v s . r . D i f f e r e n t I n s e r t i o n Depths; F r o n t SFP (y t 0 ) . 75 3 .14 R e l a t i v e Cannula PTPA v s . r ; F r o n t SFP 77 3 .15 S p a t i a l Arrangement o f t h e Motor U n i t Model . . . . . . . . . . . 79 3 .16 R e l a t i v e Cannula P o t e n t i a l v s . z ; F r o n t SFP and MUP . . 82 3 .17 PTPA v s . r , Complete CNE; F r o n t SFP and MUP 84 3 .18 SD v s . r , Complete CNE; F r o n t SFP and MUP 86 3 .19 Type I New Design 88 3 .20 Type I I New Design 88 3 .21 R e l a t i v e Cannula P o t e n t i a l v s . z , R e g u l a r and Type I / I I ; F r o n t SFP 90 3 .22 R e l a t i v e Cannula P o t e n t i a l v s . z , Regular and Type I ; MUP . . . . 92 3 .23 R e l a t i v e Cannula P o t e n t i a l v s . r , R e g u l a r and Type I / I I ; F r o n t SFP and MUP 93 3 .24 PTPA v s . r , Regular and Type I / I I ; F r o n t SFP 95 3 .25 PTPA v s . r , R e g u l a r and Type I / I I ; MUP 96 3 .26 R e l a t i v e PTPA v s . r . R e g u l a r and Type I / I I ; MUP 98 3 .27 SD v s . r , R e g u l a r and Type I / I I ; F r o n t SFP . . . . . . . . . . . . 99 3 .28 SD v s . r , Regular and Type I / I I ; MUP . . 101 3 . 2 9 R e l a t i v e SD v s . r , R e g u l a r and Type I / I I ; MUP 103 A . l C i r c u i t o f t h e C u r r e n t Source . . . . . . . . . . . 119 A.2 C i r c u i t o f t h e A m p l i f i e r 120 A . 3 S i g n a l Flow C i r c u i t ( I s o l a t i o n , CMR) . . . . . . 121 v i i i L I S T OF SYMBOLS Symbol AP CNE, CN e l e c t r o d e CNEMG c o r e Meaning •core & i n s u l a t i o n ' 'core v s . remote* 'cannula v s . remote' 'core v s . c a n n u l a ' DISA EMG MU MOP PTPA PTPD SF SFEMG SFP SD a c t i o n p o t e n t i a l c o n c e n t r i c n e e d l e e l e c t r o d e c o n c e n t r i c n e e d l e e l e c t r o m y o g r a p h y t h e c e n t r a l w i r e o f the CNE the model e l e c t r o d e c o n s i s t i n g s o l e l y o f t h e c o r e t h e model e l e c t r o d e c o n s i s t i n g o f t h e c o r e s u r r o u n d e d by t h e i n s u l a t i o n t h e s i g n a l measured between t h e c o r e and t h e r e f e r e n c e e l e c t r o d e , w i t h t h e complete CNE the s i g n a l measured between t h e c a n n u l a and t h e r e f e r e n c e e l e c -t r o d e , w i t h t h e complete CNE the d i f f e r e n t i a l s i g n a l measured between t h e c o r e and the c a n n u l a w .r.t. t h e r e f e r e n c e e l e c t r o d e , w i t h t h e complete CNE ma n u f a c t u r e r o f e l e c t r o m y o g r a p h i c e l e c t r o d e s e l e c t r o m y o g r a p h y motor u n i t motor u n i t p o t e n t i a l peak-to-peak a m p l i t u d e , peak-to-peak d u r a t i o n s i n g l e f i b e r s i n g l e f i b e r e l e c t r o m y o g r a p h y s i n g l e f i b e r p o t e n t i a l s p i k e d u r a t i o n F i r s t o c c u r r e n c e o r e x p l a n a t i o n , page 2 13 15 i i , 16 39 40 61 61 61 41 2 4 7 8 , 56 8 , 56 4 12 7 8 , 56 ix ACKNOWLEDGEMENTS I s h o u l d l i k e t o e x p r e s s my g r a t i t u d e t o Dr. P e t e r D. Lawrence. W i t h o u t h i s c o n s t a n t encouragement and i n v a l u a b l e s u g g e s t i o n s t h e p r o j e c t and t h i s documentation would never have been p o s s i b l e . Many thanks t o C h r i s S h e f f i e l d and Dave F l e t c h e r who a s s i s t e d me d u r i n g t h e c o n s t r u c t i o n o f t h e e x p e r i m e n t a l a p p a r a t u s . I am a l s o g r a t e f u l t o Kathy Brindamour and G a i l Hrehorka f o r t h e i r f a s t and e f f i c i e n t t y p i n g o f t h e t h e s i s . My s t a y i n Canada was made p o s s i b l e by a UBC Graduate St u d e n t F e l l o w s h i p . 1 I do not knew what I may appear t o t h e w o r l d , but t o m y s e l f I seem t o have been o n l y a boy p l a y i n g on t h e s e a s h o r e , and d i v e r t i n g m y s e l f i n now and the n f i n d i n g a smoother p e b b l e o r a p r e t t i e r s h e l l t h a n o r d i n a r y , w h i l s t t h e g r e a t ocean o f t r u t h l a y a l l u n d i s c o v e r e d b e f o r e me. I s a a c Newtdn (Memoirs o f Newton, Br e w s t e r ) I . INTRODUCTION 2 1.1 The Muscle For w e l l o v e r two hundred y e a r s , b e g i n n i n g w i t h t h e f r o g l e g e x p e r i m e n t s o f L u i g i G a l v a n i , i t has been known t h a t a muscle c o n t r a c t i o n i s accompanied by some s o r t o f e l e c t r i c a l a c t i v i t y . Today e l e c t r o m y o g r a p h y (EMG), t h e measure-ment and r e c o r d i n g o f t h i s " e l e c t r i c a l a c t i v i t y " , i s a w e l l e s t a b l i s h e d and v a l u a b l e t o o l f o r t h e d i a g n o s i s o f neuromuscular d i s o r d e r s . Improved measure-ment t e c h n i q u e s , s i g n a l a n a l y s i s and experiments have l e d t o a p r o f o u n d know-led g e o f the e l e c t r o c h e m i c a l p r o c e s s e s i n v o l v e d i n t h e i n i t i a t i o n o f muscular c o n t r a c t i o n s . Membranes o f e x c i t a b l e c e l l s , i . e . nerve and muscle c e l l s , a r e e l e c t r i c -a l l y more n e g a t i v e i n s i d e t h a n o u t s i d e . T h i s i s due t o an e q u i l i b r i u m o f d i f -f u s i o n , osmotic and e l e c t r o s t a t i c f o r c e s o f t h e i o n i c c e l l and body f l u i d ( N a + , C I " , K +, p r o t e i n i o n s and o t h e r s ) and a l s o ' due t o an a c t i v e i o n t r a n s p o r t system - t h e s o - c a l l e d sodium-potassium pump. The p o t e n t i a l d i f f e r e n c e a c r o s s t h e membrane i s n o r m a l l y i n t h e o r d e r of 60 mV t o 90 mV, c a l l e d t h e r e s t i n g p o t e n t i a l . An a c t i o n p o t e n t i a l (AP) i s a temporary change o f t h e r e s t i n g p o t e n t i a l whose p o l a r i t y i s r e v e r s e d f o r a s h o r t p e r i o d o f t i m e , see F i g . 1.1. The AP, c h a r a c t e r i z e d by l o c a l i o n i c c u r r e n t f l o w s , i s made p o s s i b l e by changes o f the membrane r e s i s t i v i t y t o t h e v a r i o u s i o n s , which i s i n i t i a t e d by a s m a l l change i n t h e r e s t i n g p o t e n t i a l . I n a muscle f i b e r t h i s change i s c a l l e d t h e end p l a t e p o t e n t i a l (EPP). The motor end p l a t e i s u s u a l l y l o c a t e d midway between t h e ends o f the muscle f i b e r . As F i g . 1.1 shows, the AP i s o n l y a s h o r t temporary change a f t e r which t h e r e s t i n g p o t e n t i a l i s r e s t o r e d . The l o c a l changes t r i g g e r a " c h a i n r e a c t i o n " so t h a t an AP t r a v e l s a l o n g t h e f i b e r a t a c e r t a i n v e l o c i t y 1 d e p a r t i n g i n e i t h e r d i r e c t i o n from t h e motor end The p r o p a g a t i o n v e l o c i t y o f AP's i n the human b i c e p s b r a c h i i i s on average about 4 m/s, see s e c t i o n 1.2. 3 + 5 0 > K barrier down, K* leaves cell Na* barrier restored J 3 E - 7 0 1 Na* barrier J down, Na* \ enters cell j **- / hreshold (citation 5 / V Excess K* out of cell-diffusion of ions and sodium-potassium pump restores ionic balance J 1 i t Shock applied Time (msec) The t ransmembrane v o l t a g e and t h e I o n i c f l u x e s d u r i n g the a c t i o n p o t e n t i a l . From C a r l s o n (1977 ) , p . 4 1 . p l a t e . The AP i s absorbed a t t h e end of the muscle f i b e r and i s t h e r e f o r e n ot r e f l e c t e d . An AP r e l e a s e s C a + + i n t o the c y t o p l a s m o f t h e muscle f i b e r and t r i g g e r s a s e r i e s o f ev e n t s t h a t r e s u l t i n a muscle f i b e r c o n t r a c t i o n . A s i n g l e AP w i l l produce a s i n g l e muscle f i b e r t w i t c h . The r a t e o f f i r i n g o f 4 AP's as w e l l as the number o f muscle f i b e r s i n v o l v e d determine t h e s t r e n g t h and smoothness of a whole muscle c o n t r a c t i o n . A motor u n i t (MU) i s a number o f s i n g l e muscle f i b e r s 2 and t h e cc-motorneuron t h a t i n n e r v a t e s them. T h e r e f o r e , a l l f i b e r s b e l o n g i n g t o one MU c o n t r a c t i n c o n c e r t . Each muscle c o n t a i n s many MU's. A f f e r e n t and e f f e r e n t n e u r a l a c t i v i t y a l l o w s an a c c u r a t e f u n c t i o n i n g o f a muscle i n terms of s t r e n g t h , movement and th e i n t e r p l a y w i t h o t h e r m u s c l e s . With t r a i n i n g i t i s e a s i l y p o s s i b l e t o v o l u n t a r i l y a c t i v a t e one s i n g l e MU, f o r example i n t h e b i c e p s b r a c h i i muscle which i s f r e q u e n t l y sampled i n human r o u t i n e EMG. There e x i s t s a c o n s i d e r a b l e body o f l i t e r a t u r e t h a t d i s c u s s e s neuromuscular anatomy and p h y s i o l o g y i n d e t a i l . 1.2 The S i n g l e F i b e r Model The c h a r a c t e r i s t i c c u r r e n t s t h a t f l o w d u r i n g an AP, s p r e a d i n t o t h e t i s s u e s u r r o u n d i n g t h e muscle f i b e r . There they c r e a t e a time v a r y i n g p o t e n t i a l f i e l d w hich can be sampled by e l e c t r o d e s i n s e r t e d i n t o t h e m u s c l e . The p o t e n t i a l measured e x t r a c e l l u l a r l y (when the e l e c t r o d e does not e n t e r t h e c e l l ) i s d i f -f e r e n t from t h e p o t e n t i a l a c r o s s t h e c e l l membrane as d e p i c t e d i n F i g . 1.1. T h e o r e t i c a l l y , innumerable models c o u l d s i m u l a t e t h e e x t r a c e l l u l a r l y p i c k e d up p o t e n t i a l shape. The model t h a t i s f r e q u e n t l y u s ed today t o d e s c r i b e t h e b i o -l o g i c g e n e r a t o r and t h e muscle t i s s u e , was b a s i c a l l y d e v e l o p e d by L o r e n t e de N6 (1947) and was l a t e r r e f o r m u l a t e d by R o s e n f a l c k (1957) and P l o n s e y (1969). A s i n g l e muscle f i b e r (SF) can s i m p l y be modeled as a d i p o l e g e n e r a t o r o f con-s t a n t c u r r e n t I , which t r a v e l s a l o n g the muscle f i b e r a t t h e p r o p a g a t i o n The average number of f i b e r s w i t h i n a MU can v a r y from a few t o many hundred f i b e r s , see s e c t i o n 1.2. v e l o c i t y of an AP. The muscle t i s s u e i s r e p r e s e n t e d by a homogenous and i s o -t r o p i c volume c o n d u c t o r o f s p e c i f i c c o n d u c t i v i t y a. In r e a l i t y , homogeneity and i s o t r o p y do not q u i t e a p p l y , and t h e s p e c i f i c c o n d u c t i v i t y (or r e s i s t i v i t y ) i s n o n - l i n e a r and f r e q u e n c y dependent. The volume c o n d u c t o r i s r e p r e s e n t e d by a p h y s i o l o g i c a l 0.9% s a l i n e s o l u t i o n . The p o t e n t i a l ( F i g . 1.2) a t a p o i n t P i n a c y l i n d r i c a l c o o r d i n a t e system ( z , r ) w i t h t h e c e n t r e o f t h e d i p o l e i n i t s o r i g i n i s g i v e n by where a i s t h e c o n d u c t i v i t y o f the s a l i n e , 2s t h e d i p o l e l e n g t h and I t h e c o n -s t a n t c u r r e n t . The s o u r c e and s i n k (±1) o f t h e d i p o l e i n t h e l a b o r a t o r y model ( 1 . 1 ) r z r 5 0 s -I O z F I q u r e 1 .2 . The s i n g l e f i b e r d i p o l e c o n c e p t . c o n s i s t o f two s m a l l m e t a l spheres o f d i a m e t e r 2a, c o r r e s p o n d i n g t o t h e diameter of a muscle f i b e r . The p h y s i c a l l i m i t a t i o n imposed by the f i n i t e s i z e o f the spheres does not a f f e c t t h e problem, f o r th e f i e l d w i l l o n l y be 6 c o n s i d e r e d where r > a. The v a l u e s o f I and a determine the a b s o l u t e p o t e n t i a l whereas s i n f l u e n c e s the shape o f the p o t e n t i a l f i e l d . E x p e r i m e n t a l l y o b t a i n e d v a l u e s from the human b i c e p s b r a c h i i muscle g i v e an average o f s = 0.25 mm ( d i p o l e l e n g t h 2s = 0.5 mm)/ a — 0.025 mm (d i a m e t e r o f a muscle f i b e r 2a — 0.05 mm) and a p r o p a g a t i o n v e l o c i t y o f about 4 m/s; see B u c h t h a l (1955), E k s t e d t (1964), R o s e n f a l c k (1969) and Boyd e t a l . (1978). F i g u r e 1.3 d e p i c t s a group o f i s o p o t e n t i a l l i n e s ( o f which t h e r e i s an i n f i n i t e number) t o i l l u s t r a t e t h e manner i n which the p o t e n t i a l f i e l d i s d i s -t r i b u t e d around the d i p o l e , a c c o r d i n g t o Eqn. 1.1 and F i g . 1.2. -> z F I q u r e 1 .3 . The d i p o l e and the p o t e n t i a l d i s t r i b u t i o n ( I s o p o t e n t i a l l i n e s ) . From Geddes (1972 ) , p. 27 1. In F i g . 1.4 two e x t r a c e l l u l a r AP's a r e shown as a f u n c t i o n o f z, r e c o r d e d a t two d i f f e r e n t d i s t a n c e s x1 and r 2 p a r a l l e l t o t h e a x i s o f t h e f i x e d d i p o l e g e n e r a t o r . I t s h o u l d be n o t e d t h a t t h e AP f o r r 2 has a s m a l l e r a m p l i t u d e and l e s s pronounced "peak" t h a n f o r r , . F 1 g u r e 1.4 . An e x t r a c e l l u l a r a c t i o n p o t e n t i a l e n c o u n -t e r e d by e x p l o r i n g e l e c t r o d e moving a l o n g l i n e s r, , r 2 p a r a l l e l to the d i p o l e a x i s ( F 1 g . 1 . 3 ) . From Geddes ( 1 9 7 2 ) , p. 271 . The e x t r a c e l l u l a r l y r e c o r d e d AP's d e s c r i b e d so f a r o r i g i n a t e from a s i n g l e muscle f i b e r g e n e r a t o r and a r e r e f e r r e d t o as s i n g l e f i b e r p o t e n t i a l s ( S F P ) . The s i n g l e f i b e r s b e l o n g i n g t o a MU always f i r e t h e i r i n d i v i d u a l AP's n e a r l y s i m u l t a n e o u s l y so t h a t t h e accompanying p o t e n t i a l f i e l d s a r e superimposed t o form the s o - c a l l e d motor u n i t p o t e n t i a l (MUP). I t s a m p l i t u d e i s g e n e r a l l y h i g h e r and i t s shape l e s s " s p i k y " than a SFP but b o t h a m p l i t u d e and shape of a MUP depend v e r y much on t h e number and s p a t i a l arrangement o f t h e c o n s t i t u t i n g f i b e r s as w e l l as on t h e p o s i t i o n of the s a m p l i n g e l e c t r o d e r e l a t i v e t o t h e MU. More i n f o r m a t i o n about MUP's i s g i v e n i n s e c t i o n 3.8. The nomenclature of d i s t i n c t AP f e a t u r e s i s shown i n F i g . 1.5. I t s h o u l d be noted t h a t the r e c o r d e d AP shape i s i d e n t i c a l when the e x p l o r i n g e l e c t r o d e samples t h e f i e l d o f t h e f i x e d d i p o l e a l o n g a l i n e p a r a l l e l t o t h e d i p o l e a x i s (AP as a f u n c t i o n o f z; F i g . 1.4) o r when a f i x e d e l e c t r o d e samples t h e f i e l d o f the d i p o l e moving by a l o n g i t s a x i s (AP as a f u n c t i o n o f t i m e , c o r r e s p o n d i n g t o r e a l i t y ; F i g . 1.5). The c o n v e r s i o n f a c t o r of t h e time and z - a x i s i s the AP p r o p a g a t i o n v e l o c i t y . 8 voltage , Baseline Intersection ... N A Peak J \ time 1 *> 1 a. , 1 Trough : i v/ Pot. Pnase ' Nez. Phase i Terminal Phases 1 I I i 1 Rising phue i j Rise-time j ! n : J Spike duration 1 • i F I g u r e 1.5. A c t i o n p o t e n t i a l n o m e n c l a t u r e : " s p i k e " d e -n o t e s the f a s t p o s i t i v e - n e g a t i v e p h a s e s o f a c l e a n , smooth AP of the t y p e shown. I t i s o n l y a s s i g n e d to the AP s h a p e , and i s u s e d I r r e s p e c t i v e o f i t s b e i n g g e n e r a t e d by one o r s e v e r a l f i b e r s . The s p i k e v o l t a g e 1s a l s o c a l l e d p e a k - t o - p e a k a m p l i t u d e and the r i s e t ime p e a k - t o - p e a k d u r a t i o n . From E k s t e d t ( 1964 ) , p . 30 . 1.3 L i m i t a t i o n s o f t h e L a b o r a t o r y S i n g l e F i b e r Model A d i p o l e g e n e r a t o r suspended i n an e l e c t r o l y t i c s o l u t i o n does not e x a c t l y r e p r o d u c e AP's as e n c o u n t e r e d i n r e a l muscle (see f o r example R o s e n f a l c k , 1969, p . 6 5 ) . T h i s i s no h a n d i c a p s i n c e the main purpose o f t h e i n v e s t i g a t i o n was t h e comparison o f measurement r e s u l t s . As l o n g as t h e model param e t e r s remain unchanged, r e l e v a n t c o n c l u s i o n s can be drawn. The model cannot s i m u l a t e t h e f r e q u e n c y b e h a v i o u r o f r e a l EMG. The d i p o l e g e n e r a t o r c o u l d not be c o n v e n i e n t l y moved a t a g i v e n v e l o c i t y t o s i m u l t a n e o u s l y r e c o r d t h e AP as a t i m e - v a r y i n g s i g n a l w i t h an e l e c t r o d e a t a c e r t a i n l o c a t i o n . Rather, t h e d i p o l e remained a t a f i x e d p o s i t i o n whereas t h e e l e c t o d e sampled t h e p o t e n t i a l a t a number of d i f f e r e n t p o i n t s ( z , r ) . The AP as a f u n c t i o n o f time c o u l d be r e g a i n e d by d i v i d i n g t h e d i s t a n c e z by t h e AP p r o p a g a t i o n v e l o c i t y . However, the f r e q u e n c y e f f e c t s cannot be r e s t o r e d f o r two r e a s o n s : ( i ) SFP's from c l o s e f i b e r s a r e v e r y " s p i k y " . They c o n t a i n main 9 f r e q u e n c y components of up t o 10 kHz ( S t S l b e r g & T r o n t e l j , 1979). The p r o c e s s e s t a k i n g p l a c e a t t h e e l e c t r o d e - e l e c t r o l y t e i n t e r f a c e , which are d i s c u s s e d i n s e c t i o n 2.4, a r e f r e q u e n c y dependent. Y e t t h e measurements were c a r r i e d o u t q u a s i - s t a t i o n a r i l y . T h e r e f o r e , t h e f r e q u e n c y dependence of the c o n c e n t r i c n e e d l e e l e c t r o d e f o r t h e near f i e l d c o u l d n o t be taken i n t o a c c o u n t . However, SFP's from more d i s t a n t f i b e r s a r e "smoothed" o u t due t o the n a t u r e of the p r o p a g a -t i o n o f the volume c o n d u c t o r c u r r e n t s a c c o r d i n g t o Eqn. 1.1; see a l s o F i g . 1.4. Hence the f a r f i e l d has a s t r o n g l y r e d u c e d f r e q u e n c y power spectrum ( S t a l b e r g & T r o n t e l j , 1979) and can be c o n s i d e r e d q u a s i - s t a t i o n a r y . T h e r e f o r e t h e l i m i t a t i o n s o f t h e model i n terms of f r e q u e n c y a f f e c t e d o n l y the near f i e l d , ( i i ) The volume c o n d u c t o r i t s e l f (the muscle t i s s u e ) i s not p u r e l y r e s i s -t i v e b u t c o n t a i n s f r e q u e n c y dependent elements (Schwan, 1957 & 1963; P l o n s e y , 1969). T h e r e f o r e , the r a d i a l d e c l i n e o f t h e AP i s f r e q u e n c y dependent (Gath & S t a l b e r g , 1978; S t a l b e r g & T r o n t e l j , 1979). Because of th e q u a s i - s t a t i o n a r y n a t u r e o f the model measurements, a l s o t h o s e f r e q u e n c y e f f e c t s c o u l d n o t be t a k e n i n t o a c c o u n t . Motor u n i t s have a n o t h e r p r o p e r t y t h a t a f f e c t s t h e shape of t h e r e c o r d e d MUP: s l i g h t l y d i f f e r e n t p r o p a g a t i o n v e l o c i t i e s i n both t h e motorneuron axons and the muscle f i b e r s , and a l s o v a r y i n g l o c a t i o n s o f t h e i n n e r v a t i o n s i t e s ( a l o n g t h e muscle f i b e r ) cause a s o - c a l l e d d i s p e r s i o n o f AP's. I t means t h a t i n a p l a n e p e r p e n d i c u l a r t o t h e a x i s of the muscle f i b e r s t h e i n d i v i d u a l AP's o f t h e f i b e r s b e l o n g i n g t o t h e same MU do n o t a r r i v e a l l a t t h e same t i m e . The e f f e c t on t h e MUP i s a f u r t h e r s p r e a d r e s u l t i n g i n a l o n g e r d u r a t i o n . The model a t t h i s s t a g e c o u l d not take d i s p e r s i o n i n t o a c c o u n t because t h e p o t e n t i a l s were r e c o r d e d by hand. With d a t a s t o r a g e on tape o r d i s k and 10 computer-aided s i g n a l a n a l y s i s the d i s p e r s i o n element c o u l d e a s i l y be i n t r o -duced. 1.4 EMG E l e c t r o d e s The most e s s e n t i a l d e s i r a b l e p r o p e r t y o f an EMG e l e c t r o d e i s i t s a b i l i t y t o l e a d o f f t h e d e s i r e d q u a n t i t y (SFP, MUP, g r o s s muscle a c t i v i t y ) c o n s i s t e n t l y f r e e o f d i s t o r t i o n . I t i s o b v i o u s t h a t no " u n i v e r s a l " e l e c t r o d e can f u l f i l l a l l m e c h a n i c a l and e l e c t r i c a l c r i t e r i a : ( i ) M e c h a n i c a l l y , t h e e l e c t r o d e must not c r u s h any f i b e r s but r a t h e r push them a p a r t so t h a t t h e l e a d i n g - o f f s u r f a c e o f t h e e l e c t r o d e i s p o s i -t i o n e d i n t e r s t i t i a l l y . Damaged f i b e r s c a r r y i r r e g u l a r AP's o r none a t a l l . Moreover, the p r o p e r t i e s o f t h e volume c o n d u c t o r i n the v i c i n i t y o f a c r u s h e d f i b e r a r e a l t e r e d because o f a d i s t u r b e d i o n i c e q u i l i b r i u m . T h i s i n t u r n would l e a d t o a m i s i n t e r p r e t a t i o n o f t h e r e c o r d e d a c t i v i t y , e s p e c i a l l y because t h e muscle f i b e r s c l o s e s t t o t h e l e a d i n g - o f f s u r f a c e g i v e r i s e t o t h e most s i g n i f i c a n t p o r t i o n o f an AP. ( i i ) E l e c t r i c a l l y , n e i t h e r the n e e d l e nor t h e l e a d i n g - o f f s u r f a c e s h o u l d i n t e r a c t w i t h t h e o r i g i n a l p o t e n t i a l d i s t r i b u t i o n i n t h e t i s s u e . Otherwise t h e r e c o r d e d s i g n a l does not e x a c t l y c o r r e s p o n d t o t h e " t r u e " s i g n a l when no e l e c t r o d e i s i n t h e t i s s u e . Those q u e s t i o n s a r e d i s c u s s e d i n s e c t i o n s 1.6 and 2.4. I n a d d i t i o n , t h e e l e c t r o d e -a m p l i f i e r system s h o u l d i d e a l l y have a t r a n s f e r f u n c t i o n o f p u r e g a i n K. Those and o t h e r q u e s t i o n s c o n c e r n i n g t h e e l e c t r i c a l s i g n a l p r o -c e s s i n g are t r e a t e d i n s e c t i o n 2.6. Apart from t h e c o n c e n t r i c n e e d l e e l e c t r o d e , which i s d e s c r i b e d i n d e t a i l i n t h e next s e c t i o n , many o t h e r EMG e l e c t r o d e s e x i s t . Each one has d i s t i n c t 11 p r o p e r t i e s r e l a t e d t o ( i ) and ( i i ) above, and s e r v e s a c c o r d i n g l y v a r i o u s p u r -p o s e s . The f o l l o w i n g p a r a g r a p h summarizes b r i e f l y t h e c o n s t r u c t i o n and p r o p e r -t i e s o f a few p o p u l a r EMG e l e c t r o d e s . More d e t a i l s can be f o u nd i n t h e a p p r o -p r i a t e l i t e r a t u r e . The monopolar n e e d l e s i m p l y c o n s i s t s of an i n s u l a t e d t h i n s t a i n l e s s s t e e l n e e d l e w i t h a s m a l l c o n i c a l bare t i p . The s i g n a l i s r e c o r d e d between the t i p and a r e f e r e n c e e l e c t r o d e , u s u a l l y i n the form o f a s k i n o r subcutaneous e l e c -t r o d e . The monopolar n e e d l e e l e c t r o d e i s o f v a l u e as a s e a r c h i n g t o o l because o f i t s o m n i d i r e c t i o n a l p r o p e r t i e s . I t y i e l d s t h e h i g h e s t a m p l i t u d e s o f a l l EMG e l e c t r o d e s and the l e a s t s i g n a l d i s t o r t i o n . I t s p r a c t i c a l l y u n r e s t r i c t e d p i c k -up r a d i u s r e s u l t s i n a low n o i s e r e j e c t i o n . The c h a r a c t e r i s t i c s a r e not v e r y c o n s i s t e n t because the a r e a of the c o n i c a l l e a d i n g - o f f s u r f a c e i n c r e a s e s w i t h use and a l s o because the i n s u l a t i o n can sometimes break c r e a t i n g f a l s e l e a d i n g -o f f s u r f a c e s . The e l e c t r o d e i s i n e x p e n s i v e and r e p a i r i n g o r r e s h a p i n g attempts a r e not worth the t r o u b l e . I t p r o v i d e s a good p a t i e n t c o m f o r t because of i t s s m a l l e r d i ameter than most of the hypodermic n e e d l e e l e c t r o d e s and because o f t h e v e r y good a n t i - f r i c t i o n p r o p e r t y of t h e T e f l o n c o a t i n g . S i m i l a r p r o p e r t i e s a r e f o u nd i n t h e f i n e w i r e e l e c t r o d e which c o n s i s t s o f one o r two f i n e i n s u l a t e d w i r e s w i t h exposed t i p s . They a r e i n s e r t e d i n t o t h e muscle w i t h a s p e c i a l t e c h n i q u e and can remain t h e r e over a l o n g p e r i o d o f t i m e . S i n c e t h e f i n e w i r e does not i n t e r a c t w i t h the motion of the muscle, t h i s t y p e of e l e c t r o d e i s u s e f u l i n k i n e s i o l o g i c a l s t u d i e s . U n f o r t u n a t e l y , t h e f i n e w i r e does not have v e r y c o n s i s t e n t c h a r a c t e r i s t i c s , p i c k s up much n o i s e , can wander and o c c a s i o n a l l y b reak. In the case of two c l o s e l y spaced f i n e w i r e s where t h e r e c o r d i n g i s made d i f f e r e n t i a l l y , t h e r e d u c e d p i c k u p r a d i u s and n o i s e r e j e c t i o n a r e t r a d e d f o r more d i s t o r t i o n . 12 The b i p o l a r c o n c e n t r i c n e e d l e e l e c t r o d e i s v e r y s i m i l a r i n c o n s t r u c t i o n t o the r e g u l a r c o n c e n t r i c n e e d l e e l e c t r o d e . Two f i n e w i r e s a r e embedded i n t h e lumen o f a hypodermic n e e d l e and exposed a t t h e t i p . R e c o r d i n g i s made d i f f e r e n t i a l l y between those two c e n t e r e l e c t r o d e s , which r e s u l t s i n a s m a l l p i c k u p a r e a , d i r e c t i o n a l p r o p e r t y and v e r y good S/N r a t i o . The s i g n a l , however, i s v e r y much d i s t o r t e d (almost d i f f e r e n t i a t e d ) and o n l y low a m p l i t u d e s a r e p i c k e d up. The c a n n u l a u s u a l l y s e r v e s as a ground e l e c t r o d e which improves the n o i s e r e j e c t i o n and e l i m i n a t e s the need f o r any f u r t h e r e l e c t r o d e s . The n e e d l e m u l t i e l e c t r o d e w i t h up t o 14 l e a d i n g - o f f s u r f a c e s o f c o n s i d e r -a b l e a r e a a l o n g t h e s i d e o f a hypodermic n e e d l e i s u s e f u l i n MU t e r r i t o r y s t u d i e s . I t i s done by r e c o r d i n g the same MUP from t h e v a r i o u s s u r f a c e s , t h e s p a c i n g s o f which a r e known. The l a r g e s t o f t h e m u l t i e l e c t r o d e s a r e q u i t e t h i c k (about 1 mm) and a r e t h e r e f o r e n ot v e r y c o m f o r t a b l e f o r t h e p a t i e n t . The s i n g l e f i b e r n e e d l e e l e c t r o d e e x h i b i t s an e x t r e m e l y s m a l l p i c k u p a r e a ( c o n t a i n i n g o n l y one o r two f i b e r s ; S t i l b e r g & T r o n t e l j , 1979) and a pronounced d i r e c t i o n a l p r o p e r t y . T h i s i s a c h i e v e d by a v e r y s m a l l l e a d i n g - o f f s u r f a c e on t h e o r d e r o f t h e d i a m e t e r o f a s i n g l e muscle f i b e r . R e c o r d i n g i s made between t h i s s m a l l s u r f a c e , embedded i n i n s u l a t i n g epoxy r e s i n i n a s i d e p o r t n e a r t h e t i p o f t h e hypodermic n e e d l e , and the n e e d l e as r e f e r e n c e . T h i s c o n f i g u r a t i o n i n t r o d u c e s much l e s s d i s t o r t i o n t h a n t h e b i p o l a r c o n c e n t r i c n e e d l e e l e c t r o d e . S i n g l e f i b e r e l e c t r o d e s a l l o w t h e r e c o r d i n g o f a SFP even d u r i n g s t r o n g muscle c o n t r a c t i o n w i t h many MU's i n v o l v e d . The h i g h e l e c t r o d e impedance r e q u i r e s a h i g h q u a l i t y r e c o r d i n g equipment. E x t e n s i v e i n f o r m a t i o n about SFEMG can be found i n E k s t e d t (1964) and S t a l b e r g & T r o n t e l j ( 1 9 7 9 ) . With t h e e x c e p t i o n o f the b i p o l a r c o n c e n t r i c n e e d l e e l e c t r o d e , a l l EMG e l e c t r o d e s r e q u i r e a se c o n d e l e c t r o d e e i t h e r as i n d i f f e r e n t / r e f e r e n c e o r as a ground e l e c t r o d e . U s u a l l y s k i n o r subcutaneous e l e c t r o d e s s e r v e t h a t p u r p o s e . 13 Those e l e c t r o d e s are o c c a s i o n a l l y used a l s o f o r t h e o b s e r v a t i o n o f compound muscle AP's i n motor n e r v e c o n d u c t i o n t e s t s and o f g r o s s EMG a c t i v i t y . 1.5 The C o n c e n t r i c Needle E l e c t r o d e S i n c e A d r i a n & Bronk (1929) i n t r o d u c e d t h e c o n c e n t r i c n e e d l e e l e c t r o d e (CNE) f o r e l e c t r o m y o g r a p h i c measurements, i t has been t h e most f r e q u e n t l y used type of e l e c t r o d e f o r r o u t i n e EMG u n t i l t o d a y . I t c o n s i s t s o f a b a r e , s t a i n l e s s s t e e l hypodermic n e e d l e t h e lumen o f which c o n t a i n s a t h i n p l a t i n u m w i r e embedded i n i n s u l a t i n g epoxy r e s i n . A t t h e d i s t a l end t h e w i r e , t h e i n s u l a t i o n and t h e n e e d l e a r e c u t a t an a n g l e of about 15° t o t h e s h a f t so t h a t t h e exposed p l a t i n u m c e n t e r e l e c t r o d e becomes e l l i p t i c a l and i s f l u s h w i t h t h e a l s o e l l i p t i c a l , a n n u l a r i n s u l a t i o n and c a n n u l a , see F i g . 1.6. The b i a s c u t end c o n s t i t u t e s a v e r y sharp p o i n t which promotes ease of i n s e r t i o n . B e f o r e each a p p l i c a t i o n t h e t i p s h o u l d c a r e f u l l y be i n s p e c t e d f o r freedom of "hooks" so t h a t t h e i n s e r t i o n does not cause t i s s u e damage. F 1 gure 1 .6. The c o n c e n t r i c n e e d l e e l e c t r o d e . 14 The dimensions o f a p o p u l a r CNE (DISA 13L31, 13K58) are an o u t e r c a n n u l a diameter of 0.65 mm and a p l a t i n u m w i r e diameter o f 0.15 mm. The 15° a n g l e produces t h e r e f o r e an e l l i p t i c l e a d i n g - o f f s u r f a c e o f 150 ym x 580 ym. Other c a n n u l a and c e n t e r e l e c t r o d e diameters are c o m m e r c i a l l y a v a i l a b l e . The s h a f t u s u a l l y has a l e n g t h o f 20 t o 60 mm. A t t h e p r o x i m a l end t h e c e n t r a l w i r e and t h e cannula a r e a t t a c h e d t o the two i n n e r l e a d s o f a s h i e l d e d c a b l e . A s t a n d a r d DIN jack a t t h e o t h e r end p r o v i d e s c o n n e c t i o n t o t h e measuring equipment. F i g . 1.7 d e p i c t s t h e DISA 13K53 CN e l e c t r o d e . F I q u r e 1 . 7 , Photograph of the DISA 13K53 c o n c e n t r i c n e e d l e e l e c t r o d e ( s h a f t d i a m e t e r 0.45 nm). 15 M a i n l y p r a c t i c a l c o n s i d e r a t i o n s l e d t o t h e development o f t h e CNE. The t e c h n o l o g y e x i s t s f o r m a n u f a c t u r i n g hypodermic n e e d l e s t h a t a r e i n common c l i n i c a l u s e . S t a i n l e s s s t e e l i s n o t a f f e c t e d by s a l i n e and o f f e r s good m e c h a n i c a l r i g i d i t y . The b e v e l e d t i p can e a s i l y be r e g r o u n d t o ensure a con-s i s t e n t l y sharp p o i n t . In a d d i t i o n , the s t a i n l e s s s t e e l c o n s t r u c t i o n i s e a s i l y s t e r i l i z a b l e ( a u t o c l a v e or o t h e r s t e r i l i z i n g e q u ipment). 1.6 The Problem o f CNEMG Measurement D e s p i t e i t s advantageous m e c h a n i c a l p r o p e r t i e s and i t s t r a d i t i o n a l u se, t h e a p p l i c a t i o n o f t h e CNE i s l i m i t e d by i t s d i s t o r t i o n s . The s h a f t o f t h e CNE i s u s u a l l y i n s e r t e d p e r p e n d i c u l a r l y and t h e b e v e l p a r a l l e l t o t h e axes o f the f i b e r s f o r h i g h e s t a m p l i t u d e ( E k s t e d t , 1964). There a r e most l i k e l y s e v e r a l f i b e r s of an a c t i v e MU v e r y c l o s e t o any p a r t o f t h e l a r g e P t s u r f a c e , a l l o f which c o n t r i b u t e s i g n i f i c a n t l y t o t h e " s p i k e " p o r t i o n o f t h e r e c o r d e d s i g n a l . The number o f t h o s e c l o s e f i b e r s depends on t h e s p a t i a l arrangement o f t h e f i b e r s i n t h e v i c i n i t y of the l e a d i n g - o f f s u r f a c e . P r o p e r t i e s o f t h e MU a r e d i s c u s s e d i n s e c t i o n 3.8. The c i r c u m s t a n c e t h a t more than 1 or 2 f i b e r s c o n -t r i b u t e s i g n i f i c a n t l y t o t h e r e c o r d e d s i g n a l makes t h e CNE d e f i n i t e l y an e l e c -t r o d e f o r t h e s t u d y o f MUP's r a t h e r than SFP's, i n c l i n i c a l EMG ( S t a l b e r g S T r o n t e l j , 1979). I t i s known t h a t t h e CNE does n o t e x a c t l y measure t h e t r u e s i g n a l i n t h e muscle ( B u c h t h a l , 1954; E k s t e d t , 1964; S t a l b e r g & T r o n t e l j , 1979). The d i s t o r t i o n s can b a s i c a l l y be a t t r i b u t e d t o t h r e e f a c t o r s and t h e i r i n t e r p l a y . ( i ) The l a r g e , e l l i p t i c a l P t l e a d i n g - o f f a r e a o f 0.07 mm2 encompasses c o n s i d e r a b l e p o t e n t i a l d i f f e r e n c e s i n t h e t i s s u e . The s i g n a l t h a t i s l e d o f f has c o n t r i b u t i o n s from a l l p o t e n t i a l s a l o n g t h e s u r f a c e ( c f . s e c t i o n 2.4). E k s t e d t & S t a l b e r g (1973) s i m u l a t e d on a computer 16 t h e i s o l a t e d e f f e c t o f p o t e n t i a l a v e r a g i n g o f t h e e l l i p t i c a l P t s u r f a c e . ( i i ) The p r e s e n c e o f t h e CNE i n t h e t i s s u e d i s t o r t s t h e o r i g i n a l p o t e n t i a l d i s t r i b u t i o n . Two o f the mechanisms o f d i s t o r t i o n ("wall e f f e c t " and " s h u n t i n g o f volume c o n d u c t o r c u r r e n t s " ; E k s t e d t , 1964; S t a l b e r g & T r o n t e l j , 1979) are e x p l a i n e d i n s e c t i o n 2.4. No q u a n t i t a t i v e r e p o r t s about the e f f e c t s o f the p r e s e n c e o f t h e CNE ( e s p e c i a l l y t h e l a r g e c a n n u l a ) were found i n t h e l i t e r a t u r e . L u n d e r v o l d & L i (1953) and a l s o E k s t e d t (1964) presumed "no o b v i o u s d i s t o r t i n g e f f e c t " o f the c a n n u l a . ( i i i ) The s i g n a l i s measured d i f f e r e n t i a l l y between t h e c e n t r a l P t w i r e and the c a n n u l a s h a f t w.r.t. a remote ground e l e c t r o d e . I t i s g e n e r a l l y assumed t h a t the c a n n u l a p o t e n t i a l i s low enough t o n o t a p p r e c i a b l y d i s t o r t t h e d i f f e r e n t i a l s i g n a l ( L u n d e r v o l d & L i , 1953; E k s t e d t , 1964). Another s t u d y ( B u c h t h a l , 1954) r e p o r t e d c a n n u l a p o t e n t i a l s i n the o r d e r o f 25% t o 30% of the c e n t r a l w i r e ('core') p o t e n t i a l . I f t h e c a n n u l a p o t e n t i a l has a d i f f e r e n t shape than t h e c o r e p o t e n t i a l , then t h e d i f f e r e n t i a l s i g n a l i s d i s t o r t e d i n both a m p l i t u d e and shape. The f a c t t h a t t h e c a n n u l a i s not an i d e a l r e f e r e n c e e l e c t r o d e o f z e r o p o t e n t i a l i s r e s p o n s i b l e f o r a r e s t r i c t e d p i c k u p a r e a o f t h e CNE ( c f . s e c t i o n 3.8). P o t e n t i a l s from more d i s t a n t f i b e r s a r e a p p r o x i m a t e l y e q u a l on t h e c o r e and t h e c a n n u l a and a r e t h e r e f o r e c a n c e l l e d . A r e s t r i c t e d p i c k u p a r e a i s a welcomed f e a t u r e f o r c e r t a i n a p p l i c a t i o n s ( e . g . SFEMG) b u t i s a l w a y s t r a d e d f o r d i s t o r t i o n s . The g o a l o f t h i s i n v e s t i g a t i o n was t o see i n what ways t h e s i g n a l s a r e d i s t o r t e d by t h e CNE. An e l e c t r o l y t i c tank model o f f e r e d t h e most p r a c t i c a l 17 means t o r e a c h t h a t g o a l . The m a t h e m a t i c a l model f o r an e x t r a c e l l u l a r AP i n a volume conduc t o r a l r e a d y e x i s t e d ( c f . s e c t i o n 1.2). The r e a l i z a t i o n o f the model on an e n l a r g e d s c a l e a l l o w e d t h e i n d i v i d u a l o b s e r v a t i o n o f t h e d i s t o r t i n g f a c t o r s ( i ) .. ( i i i ) , i n a s t a t i c environment. The elements t e s t e d were: • a p o i n t - s h a p e d e l e c t r o d e t h a t r e c o r d e d t h e s i g n a l s w i t h t h e h i g h e s t f i d e l i t y p o s s i b l e ( t r u e v a l u e ) . Those measurements s e r v e d as r e f e r e n c e f o r the q u a n t i f i c a t i o n o f the d i s t o r t i o n s i n t r o d u c e d by the CNE o r p a r t s t h e r e o f . • t h e e l l i p t i c l e a d i n g - o f f s u r f a c e f o r t h e a s p e c t s o f a v e r a g i n g ( i ) as w e l l as f i e l d d i s t u r b a n c e ( i i ) . • t h e i n s u l a t o r s u r r o u n d i n g t h e c o r e t o a s s e s s f i e l d d i s t u r b a n c e s ( i i ) . • t h e p r e s e n c e o f th e c a n n u l a as a f i e l d d i s t u r b i n g f a c t o r ( i i ) . • t h e s i g n a l p i c k e d up by t h e c a n n u l a , d i s t o r t i n g t h e d i f f e r e n t i a l s i g n a l ( i i i ) . The main f e a t u r e s o f an e x t r a c e l l u l a r AP (peak-to-peak a m p l i t u d e , p e a k - t o -peak d u r a t i o n , s p i k e d u r a t i o n ; a c c o r d i n g t o F i g . 1.5) s e r v e d as a b a s i s f o r t h e e v a l u a t i o n o f t h e measurement r e s u l t s . F i n a l l y , t h e q u e s t i o n a r o s e as t o whether o r not improvements of the CNE r e c o r d i n g p r o p e r t i e s were p o s s i b l e by s i m p l e measures. Those m a t t e r s a r e d e a l t w i t h i n s e c t i o n 3.10. 18 Water, water, everywhere, And a l l t h e boards d i d s h r i n k ; Water, water, everywhere. Nor any drop t o d r i n k . Samuel T a y l o r C o l e r i d g e (The A n c i e n t M a r i n e r , 2) I I . EXPERIMENTAL APPARATUS 19 The s c a l e o f t h e model was chosen t o be about 1:50 so t h a t t h e s m a l l muscle f i b e r becomes r e a s o n a b l y l a r g e but t h e e l e c t r o d e and tank dimensions were not un w i e l d y . Thus a l l p a r t s o f the e x p e r i m e n t a l a p p a r a t u s were r e l a t i v e -l y easy t o c o n s t r u c t . The a c t u a l s c a l e t u r n e d o u t t o be 1:51.336 due t o t h e a v a i l a b i l i t y o f a s t a n d a r d s i z e s t a i n l e s s s t e e l t u b i n g f o r t h e c o n s t r u c t i o n o f th e cannula model. A l l dimensions i n t h e f o l l o w i n g s e c t i o n s a r e g i v e n as %/V where £ = model v a l u e i n m i l l i m e t e r s (mm) and V = r e a l v a l u e i n micr o m e t e r s (um). 2.1 The Muscle F i b e r A n a l o g The d i p o l e model was made w i t h two s h o r t p i e c e s o f s t a i n l e s s s t e e l ( s t . St.) w e l d i n g r o d , each h a v i n g a diameter and l e n g t h of 2.57 mm / 50 um, c o r r e -s ponding t o t h e mean diameter 2a o f a s i n g l e f i b e r i n t h e human b i c e p s b r a c h i i muscle ( c f . s e c t i o n 1.2). A h o l e was d r i l l e d a x i a l l y i n t o each "bead" so t h a t t h e y c o u l d be s t r u n g onto a 1.5 mm diameter n y l o n t h r e a d . Two t h i n b r a i d e d i n s u l a t e d w i r e s were s o l d e r e d , one onto each bead t h a t i n t u r n were e p o x i e d 1 onto the t h r e a d 25.7 mm / 500 um a p a r t ( c o r r e s p o n d i n g t o t h e mean d i p o l e l e n g t h 2s, see s e c t i o n 1.2). The n y l o n t h r e a d was mounted onto a frame f i t t i n g i n t o g u i d i n g grooves i n t h e tank as e x p l a i n e d i n t h e next s e c t i o n . F i g u r e 2.1 d e p i c t s t h e d i p o l e model. 'Lepage' 5 Minute Two Component Epoxy Glue; B o u c h e r v i l l e , Canada 20 F i q u r e 2.1. The d i p o l e model . 2.2 The E l e c t r o l y t i c Tank The tank dimensions were determined by t h e a r e a o f muscle t h a t was d e s i r -a b l e t o r e p r e s e n t so t h a t the tank appeared as an " u n l i m i t e d volume c o n d u c t o r " . The w a l l s o f t h e tank d e p i c t e d b o u n d a r i e s which l i m i t e d t h e s p r e a d o f t h e p o t e n t i a l f i e l d . I f the w a l l s a r e i n s u l a t o r s , t h e n t h e i s o p o t e n t i a l l i n e s a r e p e r p e n d i c u l a r t o t h e w a l l . In c o n t r a s t , i s o p o t e n t i a l l i n e s a r e p a r a l l e l t o an e l e c t r i c a l l y c o n d u c t i v e w a l l which i s i t s e l f an e q u i p o t e n t i a l s u r f a c e (assuming z e r o v o l t a g e when the w a l l i s grounded) . I n s u l a t i n g w a l l s made out of a c r y l i c 21 Plexiglas® were chosen. The m a t e r i a l was p r a c t i c a l t o work w i t h and a l s o t r a n s p a r e n t . In a d d i t i o n , n a t u r a l muscle b o u n d a r i e s such as f a t , s k i n e t c . a r e i n s u l a t o r s r a t h e r than c o n d u c t o r s . Those b o u n d a r i e s a r e i n r e a l i t y r e l a t i v e l y f a r away i n a r a d i a l d i r e c t i o n from the MU under c o n s i d e r a t i o n , compared t o the diameter o f a SF o r even MU. The sux-face o f the s o l u t i o n w i t h a i r as an i n s u -l a t i n g boundary more or l e s s r e p r e s e n t e d r e a l i t y where t h e e l e c t r o d e was i n s e r t e d p e r p e n d i c u l a r l y . S i n c e t h e uptake r a d i u s o f t h e CNE i s l i m i t e d t o o n l y a f r a c t i o n o f a whole MU (see s e c t i o n s 1.6, 3.8) i t was n o t n e c e s s a r y t o c o n s t r u c t a v a s t tank - c o n t a i n i n g many hundred l i t e r s - t o r e p r e s e n t a com-p l e t e MU o r even muscle. A p r e l i m i n a r y tank i n d i c a t e d t h a t measurements must no t be t a k e n c l o s e r t o t h e w a l l s t h a n 150 • • • 200 mm because of f i e l d d i s t o r -t i o n s . When no measurements were made i n t h i s " b u f f e r zone" o f about 200 mm, t h e tank c o u l d be c o n s i d e r e d t o r e p r e s e n t an u n l i m i t e d volume c o n d u c t o r (see s e c t i o n 2.3). F i g u r e 2.2 shows the e l e c t r o l y t i c tank w i t h t h e nomenclature as u s e d i n the f o l l o w i n g d e s c r i p t i o n . The l e n g t h o f the tank was d e t e r m i n e d by the maximum AP d u r a t i o n . S i n c e t h e b i p h a s i c d i p o l e - g e n e r a t e d AP as r e c o r d e d e x t r a c e l l u l a r l y i s s y m m e t r i c a l about the c e n t e r o f the d i p o l e , t h e r e was no need t o r e c o r d b o t h the p o s i t i v e and n e g a t i v e p hase. The o v e r a l l l e n g t h of t h e tank was 800 mm l e a v i n g z » 400 mm e f f e c t i v e l y (when the " b u f f e r zones" were t a k e n i n t o a c c o u n t ) . 400 mm c o r -responded t o a r e a l l e n g t h of about 7800 p o r a time span o f about 2 ms a t an AP p r o p a g a t i o n v e l o c i t y of 4 m/s. The h e i g h t and depth o f the tank, on the o t h e r hand, were g i v e n by the maximum r e c o r d i n g d i s t a n c e r ( s e c t i o n 3.1). T h i s a l s o d e t e r m i n e d the c r o s s - s e c t i o n o f a p o s s i b l e MU model o r p a r t t h e r e o f . S i n c e t h e s p r e a d around a s i n g l e f i b e r was c y l i n d r i c a l l y s y m m e t r i c a l , i t was o n l y n e c e s s a r y t o r e c o r d the AP's i n a h e m i c y l i n d r i c a l a r e a . The measurement o f the d i r e c t i o n a l b e h a v i o u r of the CNE was s i m p l y done by t u r n i n g t h e s h a f t 22 F i g u r e 2 . 2 . Photograph of t h e e l e c t r o l y t i c tank (above) and tank n o m e n c l a t u r e ( b e l o w ) . 23 180° around i t s a x i s . Thus, the f i b e r , a n a l o g c o u l d be p l a c e d c l o s e r t o the back w a l l t h a n t o the f r o n t w a l l . Then the m e asuring zone from t h e s m a l l e s t t o t h e l a r g e s t r e c o r d i n g d i s t a n c e r was c e n t e r e d about the depth ( h o r i z o n t a l l y ) o f t h e tank which was 600 mm o v e r a l l l e a v i n g 200 mm / 3900 ym e f f e c t i v e l y . The h e i g h t of the tank was a l s o 600 mm l e a v i n g 200 mm e f f e c t i v e l y . So t h e maximum p o s s i b l e c r o s s s e c t i o n was 40,000 mm2 / 15.15 mm2. The muscle f i b e r model was mounted onto a frame which f i t v e r t i c a l l y i n t o t h e tank, c f . F i g . 2.2. The f i b e r c o u l d be anchored a t t h r e e d i f f e r e n t v e r t i c a l p o s i t i o n s which were i n t h e c e n t e r of t h e frame and 80 mm / 1557 um above and below, r e s p e c t i v e l y . F i g u r e 2.3 d e p i c t s t h e frame w i t h the muscle f i b e r a n a l o g . The a d j u s t a b l e f i b e r p o s i -t i o n and t h e v a r i a b l e e l e c t r o d e i n s e r t i o n depth a l l o w e d a s e r i e s of d i f f e r e n t r e c o r d i n g arrangements y and d. The a c t u a l v a l u e s u sed f o r measurements a r e g i v e n i n s e c t i o n 3.1. The tank c o n t a i n e d 275 SL o f 0.9% s a l i n e s o l u t i o n . In o r d e r t o p r e v e n t growth o f b a c t e r i a , f u n g i o r a l g a e 0.1% = 275g o f n - P r o p y l p - h y d r o x y b e n z o a t e Cg (OH). COO. CH 2. CH 2. C H 3 ( C a t a l o g 1980, BDH C h e m i c a l s L t d . , P o o l e , England) and 20 ppm copper s u l f a t e CuSO^ (= 8g c u p r i c s u l f a t e Cu SO^. 5 H 20) were added. The f i r s t c h e m i c a l was a n o n - e l e c t r o l y t e and d i d n o t a f f e c t t h e c o n d u c t i v i t y o f t h e s a l i n e whereas the second was i n such a low c o n c e n t r a t i o n t h a t t h e change i n c o n d u c t i v i t y was n e g l i g i b l e . The r e s u l t i n g c o n d u c t i v i t y o f t h e 0.9% s a l i n e s o l u t i o n was a » 1.2 mho/m. I t was not v e r y c r u c i a l t h a t an e x a c t v a l u e was o b t a i n e d s i n c e t h e e f f e c t i v e c o n d u c t i v i t y o f muscle t i s s u e can v a r y c o n s i d e r -a b l y , see f o r example R o s e n f a l c k (1969). The p o t e n t i a l a t any p o i n t i n an u n l i m i t e d , homogenous and i s o t r o p i c volume c o n d u c t o r v a r i e s i n v e r s e l y p r o p o r -t i o n a l l y t o a, as shown i n Eqn. 1.1. The c o n d u c t i v i t y o i s a l s o temperature dependent. No s p e c i a l e f f o r t was made t o keep the temperature c o n s t a n t which was i n the o r d e r o f 20 t o 22°C. The s a l i n e temperature remained v e r y much 24 c o n s t a n t d u r i n g one measurement s e r i e s but c o u l d v a r y from s e r i e s t o s e r i e s . From G l a s s t o n e (1949) the f o l l o w i n g temperature dependence of the c o n d u c t i v i t y o was d e v e l o p e d ° l / a 2 = 1 + ° ( T 1 ' T 2 } ( 2 , 1 ) where - T 2 i s the temperature d i f f e r e n c e o f the e l e c t r o l y t e i n °C and a an i o n dependent c o e f f i c i e n t ; a " 0.02 f o r N a C l . Hence a temperature v a r i a t i o n o f 2 5 2°C y i e l d e d a p o t e n t i a l v a r i a t i o n a t any p o i n t ( r , z ) o f 4%, a c c o r d i n g t o Eqns. 2.1 and 1.1. ' 2.3 V e r i f i c a t i o n o f t h e Tank P r o p e r t i e s I n o r d e r t o v e r i f y the p r o p e r t i e s of t h e l i m i t e d volume c o n d u c t o r i n t h e e l e c t r o l y t i c tank, a s e t of i s o p o t e n t i a l l i n e s was computed a c c o r d i n g t o Eqn. 1.1 on t h e b a s i s of the same dimensions as the model. The computed r e s u l t s were compared w i t h the e q u i v a l e n t s e t o f a c t u a l t a n k measurements. The e l e c -t r o d e used ( ' p o i n t e l e c t r o d e ' ) and the e l e c t r i c a l a p p a r a t u s a r e d e s c r i b e d i n s e c t i o n s 2.5 and 2.6. F i g u r e 2.4 shows the t h e o r e t i c a l and p r a c t i c a l r e s u l t s . P l o t t e d a r e o n l y the i s o p o t e n t i a l l i n e s [ i n u n i t s -I/4na] i n the f i r s t q u a d r a n t where z > 0 , r > 0. The d i s t o r t i o n s towards the tank w a l l s can c l e a r l y be seen. A c t u a l v a l u e s f o r a l l l a t e r measurements never exceeded r = 100 mm / 1946 um and z = 130 mm / 2530 ym. W i t h i n t h a t a r e a the measured worst case d e v i a t i o n from the t h e o r e t i c a l i s o p o t e n t i a l l i n e 1 m-* was e s t i m a t e d t o be a t most 5%. The measured c u r v e s were o b t a i n e d i n a h o r i z o n t a l p l a n e ( z , r ) w i t h t h e f i b e r i n i t s c e n t r a l p o s i t i o n ; compare t o F i g . 2.2. No measureable change i n t h e r e s u l t s of F i g . 2.4 was d e t e c t e d when b o t h the f i b e r and t h e e l e c t r o d e were p u t i n t o t h e two p o s i t i o n s 80 mm above o r below t h e c e n t e r . 2*4 G e o m e t r i c a l and P h y s i c a l S i m i l a r i t y I n t h e p r e c e d i n g s e c t i o n i t was shown t h a t t h e f i e l d d i s t r i b u t i o n i n t h e e l e c t r o l y t i c tank s a t i s f i e d the m a t h e m a t i c a l model (Eqn. 1.1) w i t h a maximum e r r o r of 5%. The q u e s t i o n a r o s e as t o whether o r not t h e s c a l e d up v e r s i o n o f t h e CNE would i n t r o d u c e the p h y s i c a l l y s i m i l a r d i s t o r t i o n s i n t h e g e o m e t r i c a l l y s i m i l a r t a n k . 26 Z AXIS (MICROMETERS) F i g u r e 2.4. The computed and p r a c t i c a l l y m e a s u r e d i s o p o t e n t i a l l i n e s , 1n u n i t s - I / 4 T T < J . 27 A d e t a i l e d d e s c r i p t i o n of t h e e l e c t r o c h e m i c a l p r o c e s s e s a t t h e m e t a l - e l e c -t r o l y t e i n t e r f a c e would have exceeded the scope o f t h i s t h e s i s . A c o n s i d e r a b l e body o f l i t e r a t u r e about e l e c t r o c h e m i s t r y e x i s t s , f o r example B o c k r i s & Reddy (1970). More s p e c i f i c i n f o r m a t i o n about m e t a l e l e c t r o d e s i s found i n Dymond (1976) and Weinmann & Mahler (1964). The f o l l o w i n g p a r a g r a p h s a d r e s s t h e s i m p l e r q u e s t i o n of whether the e l e c t r o d e i n t e r f a c e appears as an i n s u l a t i n g w a l l t o t h e e l e c t r o l y t e - an a p p r o x i m a t i o n f o r which t h e r e was a l r e a d y some ev i d e n c e ( P o l l a k , 1971). To t h e e x t e n t t h a t t h e i n t e r f a c e a p p e a r s as an i n s u l a t o r , t h e f i e l d w i l l be g e o m e t r i c a l l y s i m i l a r . The M e t a l - T i s s u e I n t e r f a c e The o v e r a l l e l e c t r o d e impedance was m a i n l y o f i n t e r e s t i n c o n n e c t i o n w i t h t h e measuring s e t - u p as d i s c u s s e d i n s e c t i o n 2.6. However, from the p o i n t o f view o f a p o s s i b l e d i s t o r t i o n o f t h e o r i g i n a l p o t e n t i a l d i s t r i b u t i o n , t h e e q u i v a l e n t c i r c u i t o f an i n f i n i t e s i m a l m e t a l - t i s s u e i n t e r f a c e p o r t i o n was i m p o r t a n t , as shown i n F i g . 2.5 ( a c c o r d i n g t o P o l l a k , 1971). The v a l u e o f t h e s p e c i f i c i m p e d a n c e Z^ i s d e p e n d e n t on v a r i o u s f a c t o r s s u c h a s t h e k i n d o f m e t a l , c o n c e n t r a t i o n of the e l e c t r o l y t e , v o l t a g e a c r o s s t h e i n t e r f a c e , e t c . ( P o l l a k , 1974 a , b ) . P o l l a k (1971) s t a t e d t h a t t h e s p e c i f i c i n t e r f a c e impedance was v e r y h i g h f o r s t a i n l e s s s t e e l , compared t o t h e r e s i s t i v i t y o f the t i s s u e p. In a n o t h e r i n v e s t i g a t i o n , P o l l a k (1974c) e x p e r i m e n t a l l y o b s e r v e d t h a t t h e e l e c t r o d e impedance of the h i g h l y p o l a r i z a b l e m e t a l s g o l d , p l a t i n u m and s t a i n l e s s s t e e l e x h i b i t e d e s s e n t i a l l y t h e same b e h a v i o u r . I t c o u l d t h e r e f o r e be c o n c l u d e d t h a t a l s o the s p e c i f i c i n t e r f a c e impedance Z^ o f a l l t h r e e m e t a l s Au, P t and s t . s t . was v e r y s i m i l a r , namely much l a r g e r t h a n t h e r e s i s t i v i t y p o f t h e t i s s u e ( o r s a l i n e s o l u t i o n ) . 28 ^ ^ ^ isopotential lines electrolyte \ \ \ \ \ \ \ Vfs). \ bpdr c Z{ dr Z j = s p e c i f i c impedance o f the m e t a l - t i s s u e I n t e r f a c e p = r e s i s t i v i t y o f t i s s u e = 1/<j b , c = c o n s t a n t s metal F i g u r e 2 . 5 , S i m p l i f i e d e q u i v a l e n t c i r c u i t o f t h e meta l -t i s s u e i n t e r f a c e . S h u n t i n g o f Volume Conductor C u r r e n t s A l o n g t h e i n t e r f a c e s u r f a c e S t h e r e a r e p o t e n t i a l d i f f e r e n c e s which can be d e s c r i b e d by the p o t e n t i a l f u n c t i o n V ( s ) f o r a m e t a l w i t h an i n f i n i t e i n t e r f a c e impedance. The g r a d i e n t o f V ( s ) i n c r e a s e s when the s u r f a c e i s c l o s e r t o t h e d i p o l e s o u r c e . The p o t e n t i a l d i f f e r e n c e s a r i s e from the v o l t a g e drop o v e r t h e r e s i s t a n c e s bpdr through which t h e volume c o n d u c t o r c u r r e n t s a r e d r i v e n from th e d i p o l e s o u r c e . The m e t a l a t t h e i n t e r f a c e i s a c o n d u c t o r and t h e r e f o r e no p o t e n t i a l d i f f e r e n c e s anywhere a l o n g i t can e x i s t i n s i d e t h e m e t a l . A r e d u c -t i o n o f t h e i n t e r f a c e impedance from i n f i n i t y t h e r e f o r e p u t s 2 ( c Z ^ d r ) p a r a l l e l t o b p d r . I f t h e s p e c i f i c i n t e r f a c e impedance Z^ i s not much l a r g e r t h a n t h e r e s i s t i v i t y p o f the e l e c t r o l y t e , t h e volume c o n d u c t o r c u r r e n t s can be shunted v i a t h e m e t a l s u r f a c e . T h i s d i m i n i s h e s t h e v o l t a g e drop o v e r bpdr which i s a d i s t o r t i o n o f the o r i g i n a l p o t e n t i a l d i s t r i b u t i o n V ( s ) . F o r t u n a t e l y , as men-t i o n e d above, P o l l a k (1971, 1974 a,b,c) found the s p e c i f i c i n t e r f a c e impedances 29 t o be v e r y l a r g e f o r the m e t a l s Au, P t , s t . s t . , compared t o t h e b u l k r e s i s -t i v i t y p o f t h e e l e c t r o l y t e . I n o r d e r t o v e r i f y P o l l a k ' s statement o f v e r y h i g h s p e c i f i c i n t e r f a c e i m p e d a n c e s Z^ f o r t h e metals Au, P t , s t . s t . , a s p e c i a l t e s t e l e c t r o d e was p r e -p a r e d . B e f o r e i t s d e s c r i p t i o n and t h e d i s c u s s i o n o f t h e r e s u l t s , two o t h e r e f f e c t s t h a t a r e c l o s e l y r e l a t e d t o t h e s h u n t i n g p r o c e s s a r e e x p l a i n e d . W a l l E f f e c t E k s t e d t (1964) p o i n t e d out the s o - c a l l e d " w a l l e f f e c t " . The t i s s u e can be c o n s i d e r e d t o be an u n l i m i t e d volume c o n d u c t o r . When an i n f i n i t e l y l a r g e i n s u l a t i n g p l a n e i s brought i n t o t h e volume c o n d u c t o r , an e l e c t r i c a l " m i r r o r image" of the so u r c e i s pr o d u c e d (see f o r example Weber, 1950, p. 215). The p o t e n t i a l a t e v e r y p o i n t on t h e i n s u l a t o r - e l e c t r o l y t e boundary i s t h e r e f o r e d o u b l e d by the s u p e r p o s i t i o n o f t h e r e a l and image f i e l d . The i n s u l a t i n g epoxy r e s i n s u r r o u n d i n g t h e l e a d i n g - o f f s u r f a c e p r o d u c e s such a " w a l l e f f e c t " a l t h o u g h due t o t h e f i n i t e i n s u l a t o r s i z e , no e x a c t d o u b l i n g a t a l l p o i n t s t a k e s p l a c e . E k s t e d t (1964) found t h a t i n t h e case o f an SF e l e c t r o d e w i t h a v e r y s m a l l , c i r c u l a r 25 ym d i a m e t e r l e a d i n g - o f f s u r f a c e t h e s u r r o u n d i n g " i n s u l a t i v e w a l l " must be o f a t l e a s t t w i c e t h e f i b e r d i a m e t e r i n o r d e r t o e x e r t a p p r o x i m a t e l y the f u l l w a l l e f f e c t f o r v e r y s m a l l r e c o r d i n g d i s t a n c e s . A w a l l e f f e c t can a l s o o c c u r on t h e l e a d i n g - o f f s u r f a c e i t s e l f ( w i t h no g e n u i n e i n s u l a t o r p r e s e n t ) i f t h e s p e c i f i c i n t e r f a c e impedances Z^ a r e v e r y l a r g e ( a p p r o a c h i n g <*>). Then no c u r r e n t s can be s h u n t e d as e x p l a i n e d i n t h e p r e c e d i n g p a r a g r a p h . The m e t a l l i c e l e c t r o d e t h e r e f o r e appears t o be an i n s u l a -t o r i n t h e e l e c t r o l y t e . I t can be e x p e c t e d t h a t some s h u n t i n g (when the m e t a l i s a " l e s s - t h a n - p e r f e e t * i n s u l a t o r ) does not c o m p l e t e l y s u p p r e s s t h i s " m e t a l l i c 30 w a l l e f f e c t " . A l s o , the s i z e and shape o f the l e a d i n g - o f f s u r f a c e and t h e r e c o r d i n g d i s t a n c e determine t h e f a c t o r by which t h e p o t e n t i a l i s i n c r e a s e d . P o t e n t i a l A v e r a g i n g The p o t e n t i a l d i s t r i b u t i o n V ( s ) a l o n g t h e i n t e r f a c e s u r f a c e S cannot be m e a s u r e d s e p a r a t e l y b u t o n l y t h e p o t e n t i a l V e on t h e m e t a l , which i s l e d o f f i n t o t h e a m p l i f i e r . V q c a n be approximated by the average o f the p o t e n t i a l s V ( s ) a l o n g t h e s u r f a c e S a c c o r d i n g t o P o l l a k (1971) V = ! / V ( s ) ds (2.2) e s S Both, w a l l e f f e c t and p o t e n t i a l a v e r a g i n g t a k e p l a c e a c c o r d i n g t o s c a l e i n t h e model because the p o t e n t i a l d i s t r i b u t i o n V ( s ) i s g e o m e t r i c a l l y s i m i l a r t o r e a l i t y . V e r i f i c a t i o n Measurements I n o r d e r t o measure the r e l a t i v e importance o f s h u n t i n g compared t o w a l l e f f e c t and a v e r a g i n g , a s p e c i a l e l e c t r o d e was c o n s t r u c t e d . I t c o n s i s t e d o f an e l l i p t i c a c r y l i c g l a s s s u r f a c e {= pure i n s u l a t o r ) i n t h e c e n t e r o f which a s m a l l c i r c u l a r s t . s t . l e a d i n g - o f f a r e a o f 0.8 mm / 15 urn d i a m e t e r was ground f l u s h w i t h the a c r y l i c g l a s s . The e l l i p s e had t h e dimensions 7.7 mm x 29.8 mm / 150 um x 580 ym c o r r e s p o n d i n g t o t h e s i z e o f t h e l e a d i n g - o f f s u r f a c e o f t h e CNE under i n v e s t i g a t i o n ; see a l s o s e c t i o n 2.5. Then a s e r i e s o f measurements o f t h e peak-to-peak amplitude v s . t h e r e c o r d i n g d i s t a n c e r was made ( c f . s e c -t i o n s 2.6, 3.1 f o r the d e s c r i p t i o n of the e l e c t r i c a l a p p a r a t u s p l u s g e n e r a l n o m e n c l a t u r e ) . These measurements took i n t o a c c o u n t o n l y t h e "pure w a l l 31 e f f e c t " a r i s i n g from the e l l i p t i c a c r y l i c s u r f a c e , as a f u n c t i o n o f t h e r e c o r d i n g d i s t a n c e r . I t c o u l d s a f e l y be assumed t h a t t h e e x t r e m e l y s m a l l s t . s t . l e a d i n g - o f f s u r f a c e a v e r a g e d o n l y a n e g l i g i b l y s m a l l p o t e n t i a l d i f f e r e n c e and t h e r e f o r e d i d not i n t r o d u c e any o t h e r d i s t o r t i o n t h a n t h e w a l l e f f e c t . Then the same e l e c t r o d e was c o v e r e d w i t h a Pt f o i l o f t h e same e l l i p t i c a l s i z e w i t h a s m a l l h o l e i n t h e c e n t e r so t h a t t h e s t . s t . l e a d i n g - o f f s u r f a c e was s t i l l exposed t o the e l e c t r o l y t e but i s o l a t e d from t h e P t f o i l . A s e r i e s of measurements (peak-to-peak a m p l i t u d e v s . r ) y i e l d e d t h e w a l l e f f e c t o f t h e " i n s u l a t o r P t " . Any d e c r e a s e i n p o t e n t i a l compared t o t h e "pure w a l l e f f e c t " p o t e n t i a l would have t o be a t t r i b u t e d t o s h u n t i n g o f volume c o n d u c t o r c u r r e n t s by t h e s p e c i f i c i n t e r f a c e i m p e d a n c e s Z^ o f P t . F o r c o m p a r i s o n , measurements o f t h e peak-to-peak amplitude v s . r were a l s o made w i t h t h e p o i n t -shaped e l e c t r o d e and the e l l i p t i c ' c o r e ' a l o n e o f the CNE ( f o r a d e s c r i p t i o n , see s e c t i o n 2 .5). The p o i n t e l e c t r o d e r e c o r d e d t h e t r u e peak-to-peak a m p l i t u d e w i t h n e i t h e r s h u n t i n g nor w a l l e f f e c t nor a v e r a g i n g ( i n s e c t i o n 2.3 i t was i l l u s t r a t e d t h a t the p o t e n t i a l d i s t r i b u t i o n i n the tank d i f f e r e d by a t most 5% from t h e t h e o r e t i c a l d i s t r i b u t i o n ) . The ' c o r e ' e l e c t r o d e was Au p l a t e d ( s e c t i o n 2.5) but s i n c e t h e h i g h l y p o l a r i z a b l e m e t a l s Au, P t and s t . s t . were r e p o r t e d t o have e s s e n t i a l l y the same impedance b e h a v i o u r ( P o l l a k , 1974c), i t was c o n c l u d e d t h a t Au, Pt or s t . s t . a l s o p o s s e s s e d the same s p e c i f i c i n t e r f a c e impedance. T h e r e f o r e t h e 'core* e l e c t r o d e i n c o r p o r a t e d a l l d i s t o r t i o n s -s h u n t i n g , w a l l e f f e c t and a v e r a g i n g . F i g u r e 2.6 compares a l l r e s u l t s o f t h e measurements d e s c r i b e d above. The c u r v e s a r e p l o t t e d i n % o f the peak-to-peak a m p l i t u d e o f t h e t r u e v a l u e ( p o i n t e l e c t r o d e = 100%) v s . the r e c o r d i n g d i s t a n c e r . The t o p cur v e (genuine i n s u l a -t o r ) r e v e a l s t h a t the f u l l f a c t o r o f 2 from the "pure w a l l e f f e c t " was o n l y 32 i o H 1 1 ' ' I ' 1 ' 1 1 ' ' 1 ' 1 1 1 1 1 1 1 1 r 1 1 1 • 1 1 1 > i 1 , , , 1 0 2 0 0 4 0 0 6 0 0 8 0 0 1 0 0 0 1 2 0 0 1 4 0 0 1 6 0 0 1 8 0 R E C O R D I N G D I S T A N C E R ( M I C R O M E T E R S ! F i g u r e 2 .6 . The PTPA v s r f o r " s h u n t i n g " , " w a l l e f f e c t " . • a v e r a g i n g " and t h e i r c o m b i n a t i o n s . In % o f the t r u e PTPA. 33 e x e r t e d where r < 50 ym. The f a c t o r f e l l r a p i d l y down t o 1.5 a t r = 150 um and f o r r > 800 um the w a l l e f f e c t caused l e s s t h a n 10% p o t e n t i a l i n c r e a s e . The second c u r v e above the base l i n e o f 100% was measured w i t h t h e " l e s s - t h a n -p e r f e c t i n s u l a t o r P t " . The w a l l e f f e c t i n c r e a s e d t h e p o t e n t i a l by a f a c t o r o f maximum 1.57 a t r •*• 25 um (see remark i n s e c t i o n 3.1) c o r r e s p o n d i n g t o a p o t e n t i a l d e c r e a s e of about 22% caused by s h u n t i n g , compared t o t h e "pure w a l l e f f e c t " . The p o t e n t i a l d e c r e a s e due t o s h u n t i n g was l e s s t h a n 10% f o r r > 200 um which i s e x p l i c i t l y shown i n the f i r s t c u r v e below the base l i n e o f 100%. The curve f o r the whole e l l i p t i c Au ' c o r e ' e l e c t r o d e i s a l s o shown. I t i n c o r p o r a t e s a l l p o t e n t i a l d i s t o r t i o n s due t o w a l l e f f e c t , s h u n t i n g and a v e r a g i n g . The net p o t e n t i a l d e c r e a s e amounted t o r o u g h l y 50% f o r r > 25 um and l e s s t h a n 10% where r > 350 pm. The measurements a l s o a l l o w e d t h e e x t r a c t i o n o f the c u r v e s f o r ' " a v e r a g i n g and s h u n t i n g combined" o r "pure a v e r a g i n g " a l o n e . Those c u r v e s , which a r e a l s o shown i n F i g . 2.6, were c a l c u l a t e d from the measured c u r v e s . As was a l r e a d y mentioned, the o n l y c o n c e r n f o r t h e g e o m e t r i c a l s i m i l a r i t y o f the model d i s t o r t i o n s was t h e s h u n t i n g p r o c e s s . F i g u r e 2.6 demonstrated t h a t a t the s m a l l e s t r e c o r d i n g d i s t a n c e e v e r u s e d ( r = 48.7 um, c f . s e c t i o n 3.1) the p o t e n t i a l d e c r e a s e due t o s h u n t i n g was o n l y about 20% and l e s s t h a n 10% where r > 200 ym. S h u n t i n g on t h e Pt o r Au s u r f a c e was always c o u n t e r a c t e d by t h e w a l l e f f e c t which had a much s t r o n g e r i n f l u e n c e on t h e p o t e n t i a l (99% p o t e n t i a l i n c r e a s e a t r = 48.7 um and 35% a t r = 200 ym) . A l s o , the "pure" p o t e n t i a l a v e r a g i n g , which was independent of s h u n t i n g and w a l l e f f e c t but c o u l d not be measured s e p a r a t e l y , had a s t r o n g e r e f f e c t t h a n s h u n t i n g (67% p o t e n t i a l d e c r e a s e a t r = 48.7 um and 22% a t r = 200 um). Another f a c t o r deemphasizes the e f f e c t o f s h u n t i n g f u r t h e r . The CNE a l s o has a genuine i n s u l a t o r s u r r o u n d i n g t h e c o r e (epoxy r e s i n , c f . s e c t i o n 1.5). 34 As mentioned p r e v i o u s l y , a w a l l e f f e c t a r i s e s from t h a t i n s u l a t o r , which has an a r e a of a t l e a s t 10 times t h a t o f t h e c o r e a r e a , and i s t h e r e f o r e much more pronounced than t h e " m e t a l l i c w a l l e f f e c t " from the Pt l e a d i n g - o f f s u r f a c e a l o n e . S h u n t i n g , however, t a k e s p l a c e o n l y a l o n g t h e P t s u r f a c e . So t h e p o t e n t i a l d e c r e a s e by s h u n t i n g amounts t o l e s s when e x p r e s s e d as a p e r c e n t a g e o f the p o t e n t i a l measured w i t h t h e ' c o r e ' s u r r o u n d e d by t h e i n s u l a t o r t h a n w i t h t h e 'core' a l o n e . The e x a c t c u r v e was not c a l c u l a t e d b u t i n t h e s e c t i o n s 3.2 t o 3.4 the combined r e s u l t s f o r t h e 'core* and 'core & i n s u l a t i o n ' CNE sub-a s s e m b l i e s a r e p r e s e n t e d . Thus, i t was c o n c l u d e d t h a t due t o t h e r e l a t i v e unimportance of s h u n t i n g a l o n g the Pt or Au l e a d i n g - o f f s u r f a c e s the model CNE c o r r e c t l y r e p r e s e n t e d the d i s t o r t i o n s i n a g e o m e t r i c a l l y s i m i l a r f a s h i o n t o r e a l i t y . 2.5 E l e c t r o d e s The f o l l o w i n g d e s i g n r e q u i r e m e n t s d e t e r m i n e d t h e n a t u r e of the v a r i o u s e x p e r i m e n t a l e l e c t r o d e s : • simple m a n u f a c t u r i n g ; • h i g h a c c u r a c y ; • good s t a b i l i t y and s t u r d i n e s s ; • ease of i n s t a l l a t i o n ( m e c h a n i c a l l y / e l e c t r i c a l l y ) ; • must p r o v i d e r e p r o d u c i b l e r e s u l t s . In F i g . 2.7 an e l e c t r o d e h o l d e r i s shown t h a t f u l f i l l s t h e l a s t two r e q u i r e -ments. The c y l i n d r i c a l s h a f t of t h e e l e c t r o d e s , of v a r i o u s d i a m e t e r s , was p r e s s e d a g a i n s t a V-shaped o p e n i n g by means of a screw. Thus the e l e c t r o d e was i n a v e r t i c a l l y s e l f - c e n t e r e d , i d e n t i c a l p o s i t i o n f o r c o n s e c u t i v e i n s t a l l a -t i o n s . The e l e c t r o d e h o l d e r had two r u n n e r s w i t h which i t s l i d a l o n g t h e z-a x i s on two s t u r d y aluminum r a i l s . The weight o f the e l e c t r o d e p r o d u c e d the 35 n e c e s s a r y f r i c t i o n t o h o l d t h e assembly f i r m l y i n p l a c e . The r a i l s i n t u r n had runners a t e i t h e r end which s l i d i n the r - a x i s on the m i l l e d upper edge o f the V2" t h i c k p l e x i g l a s tank w a l l s . F i g u r e 2.8 shows the complete e l e c t r o d e p o s i -t i o n i n g assembly. R u l e r s w i t h 1 mm d i v i s i o n s on the f i x e d p a r t s and marks on the m o b i l e p a r t s a l l o w e d the p o s i t i o n i n g of the e l e c t r o d e i n t h e c o o r d i n a t e system z, r , y/d. I t was e s t i m a t e d t h a t f o r a l l t h r e e axes z, r , y / d a p o s i t i o n i n g e r r o r o f at most 0.5 mm / 9.7 ym o c c u r r e d . I t was, o f c o u r s e , v e r y c r u c i a l t h a t f o r s m a l l r e c o r d i n g d i s t a n c e s r the e l e c t r o d e be p o s i t i o n e d as p r e c i s e l y as p o s s i b l e because o f a h i g h f i e l d g r a d i e n t . The t r a n s p a r e n c y o f t h e tank w a l l s 36 F i g u r e 2 .8 . The c o m p l e t e p o s i t i o n i n g a s s e m b l y . proved t o be p r a c t i c a l i n t h a t the e l e c t r o d e p o s i t i o n c o u l d be checked v i s u a l l y and c o r r e c t e d i f n e c e s s a r y . The P o i n t E l e c t r o d e T h i s e l e c t r o d e was used f o r r e f e r e n c e measurements as mentioned e a r l i e r . I t c o n s i s t e d of a T e f l o n i n s u l a t e d s t . s t . w e l d i n g r o d w i t h a c o n i c a l bare t i p about 1.27 mm / 25 um l o n g and t h i c k . F i g u r e 2.9 shows t h e d i s t a l end o f the p o i n t e l e c t r o d e . 37 F i g u r e 2 . 9 . The p o i n t - s h a p e d e l e c t r o d e . The P o i n t E l e c t r o d e Surrounded by an " I n s u l a t i n g W a l l " F i g u r e 2.10 shows t h i s s p e c i a l d e s i g n which was used f o r w a l l e f f e c t measurements as p r e s e n t e d i n s e c t i o n 3.2. I t was made from a V8" t h i c k s h e e t of p l e x i g l a s , w i t h an approximate diameter o f 95 mm / 1850 ym. In t h e c e n t e r of t h e sh e e t , a s m a l l c i r c u l a r s t . s t . s u r f a c e (0.8 mm / 15 ym) was ground f l u s h w i t h the p l e x i g l a s and c o n n e c t e d t o an i n s u l a t e d t h i n w e l d i n g r o d . The same e l e c t r o d e was then m o d i f i e d f o r the s p e c i a l measurements as d e s c r i b e d i n s e c -t i o n 2.4. No p i c t u r e o f the m o d i f i e d e l e c t r o d e ( t h e a c r y l i c s h e e t was m i l l e d down t o an e l l i p t i c shape o f 7.7 mm x 29.8 nun) i s shown. 38 F i g u r e 2.10. The p o i n t e l e c t r o d e s u r r o u n d e d by an * i nsu1 a t i ng wa11 " . Development of the CN E l e c t r o d e Model Each complete CN e l e c t r o d e has t h r e e fundamental c o n s t i t u e n t s ; the c e n t r a l w i r e , o r ' c o r e ' , the i n s u l a t i n g epoxy r e s i n s u r r o u n d i n g t h e c o r e , and the can-n u l a , s u r r o u n d i n g both c o r e and r e s i n i n the complete e l e c t r o d e . In o r d e r t o assess the i n d i v i d u a l p r o p e r t i e s of c o r e , i n s u l a t i o n and c a n n u l a , t h r e e e l e c -t r o d e sub-assemblies were c o n s t r u c t e d . The f i r s t assembly c o n s i s t e d s o l e l y o f the c o r e , the second was formed from a c o r e s u r r o u n d e d by i t s i n s u l a t o r , w h i l e t h e t h i r d c o r r e s p o n d e d to a complete e l e c t r o d e w i t h a c a n n u l a s u r r o u n d i n g an 39 i n s u l a t e d c o r e . A l l t h r e e a s s e m b l i e s were s e p a r a t e l y a v a i l a b l e f o r measure-ments . 'Core* The c o r e c o n s i s t e d o f an i n s u l a t e d 2 , 7.7 mm / 150 ym t h i c k b r a s s r o d whose o b l i q u e l y c u t t i p became e l l i p t i c a l w i t h minor a x i s 7.7 mm / 150 ym and major a x i s 29.8 mm / 580 ym. The t i p was p o l i s h e d w i t h f i n e sandpaper and c a r e f u l l y c l e a n e d w i t h methanol. The e l l i p t i c a l s u r f a c e r e c e i v e d a t h i n l a y e r o f p l a t e d A u 3 which was deemed most p r a c t i c a l . I n s e c t i o n 2.4 i t was c o n c l u d e d t h a t Au e s s e n t i a l l y e x h i b i t e d t h e same impedance b e h a v i o u r as P t . F i g u r e 2.11 shows the Au p l a t e d 'core' e l e c t r o d e . 2'KryIon'Enamel s p r a y p a i n t , Borden P r o d u c t s L t d . , Cobourg, Canada. 3 C a t h o d i c a l e l e c t r o p l a t i n g w i t h ' a c i d h a r d g o l d p l a t i n g s o l u t i o n ' (by Johnson Matthey & M a l l o r y L t d . , M o n t r e a l , Canada) a t about 1 t o 2 mA/cm2 f o r X/2 h. 40 •Core s I n s u l a t i o n ' F i g u r e 2.12 ( r i g h t ) d e p i c t s the co r e w i t h t h e s u r r o u n d i n g i n s u l a t i o n t h a t c o n s i s t e d o f a 25.4 mm / 494 ym diameter a c r y l i c r o d . Thus t h e major a x i s o f the e l l i p t i c i n s u l a t i o n s u r f a c e became 98.1 mm / 1910 ym. The b r a s s c o r e was Au p l a t e d as o u t l i n e d i n f o o t n o t e 3 . 4 1 F i g u r e 2.12. The 'core & I n s u l a t i o n ' ( r i g h t ) and the comp l e t e CNE ( l e f t ) . Complete E l e c t r o d e A s t a i n l e s s s t e e l t u b i n g , o u t e r d i a m e t e r 33.4 mm / 650 ym and i n n e r diameter 26.6 mm / 518 ym, was m i l l e d down t o an a n g l e of 15° so t h a t t h e l o n g o u t e r diameter o f the a n n u l a r e l l i p s e became 129 mm / 2510 ym. A 'core and i n s u l a t i o n ' assembly was g l u e d i n t o the c a n n u l a . The d i s t a l c a n n u l a t i p was sharpened t o a p o i n t of about 50° a c c o r d i n g t o DISA s p e c i f i c a t i o n s . The com-p l e t e e l e c t r o d e i s p i c t u r e d i n F i g . 2.12 ( l e f t ) . 42 T a b l e 2.1 summarizes and compares t h e dimensions o f t h e model CNE and two p o p u l a r CNE's, DISA 13L31, 13K58. TABLE 2.1 Dimensions o f t h e model and r e a l CNE. DISA 13L31/13K58 Model o u t e r c a n n u l a d i a . 650 Mm 33.4 mm/650 ym i n n e r " " N/A 26.6 mm/518 ym c e n t e r e l e c t r o d e d i a . 150 ym 7.7 mm/150 ym " " a r e a 150 um x 580 um = 0.07 mm2 7.7 mm x 29.8 mm = 180.2 mm2/0.07 mm2 The Reference E l e c t r o d e The r e f e r e n c e , i n d i f f e r e n t o r ground e l e c t r o d e i d e a l l y s a t i s f i e s two con-d i t i o n s : ( i ) i t i s so f a r away from t h e b i o l o g i c a l g e n e r a t o r t h a t i t assumes z e r o p o t e n t i a l ; ( i i ) i t has a l a r g e c o n t a c t a r e a w i t h a v e r y low impedance. V a r i o u s c o n f i g u r a t i o n s were t e s t e d . O b v i o u s l y ( i ) c o u l d n o t d i r e c t l y be f u l f i l l e d . I f t h e r e f e r e n c e e l e c t r o d e spanned a c o n s i d e r a b l e volume o f t h e tank so t h a t t h e e l e c t r o d e s u r f a c e assumed a k i n d o f "symmetric" p o s i t i o n t o th e d i p o l e g e n e r a t o r , t h e n a p o t e n t i a l c l o s e t o z e r o was assumed. T h a t i m p l i e d a l a r g e r e f e r e n c e e l e c t r o d e s u r f a c e which i n t u r n f u l f i l l e d ( i i ) a u t o m a t i c a l l y . The r e f e r e n c e e l e c t r o d e d e s i g n , which was a l s o i n f l u e n c e d by t e s t s about n o i s e i n t e r f e r e n c e from t h e environment, i s s k e t c h e d i n F i g . 2.13. I t s i m p l y con-s i s t e d o f a 3 mm diameter s t . s t . w e l d i n g r o d l a y i n g i n t h e lower back c o r n e r o f the tank over i t s f u l l l e n g t h o f 800 mm. T h i s c o r r e s p o n d e d t o a v e r y l a r g e s u r f a c e a r e a o f r o u g h l y 70 cm 2. The c o n n e c t i o n t o t h e bare s t . s t . r e f e r e n c e 43 r o d e l e c t r o d e was made w i t h an i n s u l a t e d s m a l l e r s t . s t . r o d t h a t was p o i n t -welded t o i t . The i n s u l a t i o n o f t h e l a t t e r was i m p o r t a n t t o p r e s e r v e t h e s y m m e t r i c a l arrangement of the r e f e r e n c e e l e c t r o d e as w e l l as t o reduce n o i s e i n t e r f e r e n c e . insulated st. st. rod 800 mm F I g u r e 2 . 1 3 . The r e f e r e n c e e l e c t r o d e . Treatment o f the L e a d i n g - o f f S u r f a c e V a r i o u s t e c h n i q u e s have been p r o p o s e d t o t r e a t t h e l e a d i n g - o f f s u r f a c e , a l l o f which aim a t r e d u c i n g t h e o v e r a l l impedance of the e l e c t r o d e and a t i m p r o v i n g t h e i n t e r f a c e s t a b i l i t y . Such t e c h n i q u e s i n c l u d e " e l e c t r o l y t i c c l e a n i n g " S t i l b e r g & T r o n t e l j (1979), " e l e c t r o l y t i c e t c h i n g " P o l l a k (1974c), " p r e s o a k i n g i n a w e t t i n g a gent" Wiechers e t a l . (1979), "Pt b l a c k " and "Ag c h l o r i d i n g " o r a c o m b i n a t i o n o f b o t h as p r o p o s e d by v a r i o u s a u t h o r s . 44 S i n c e t h e model e l e c t r o d e impedances were i n any c a s e v e r y low due t o t h e l a r g e c o n t a c t a r e a ( c f . 2.6), none o f t h o s e s p e c i a l t r e a t m e n t s was n e c e s s a r y . B e f o r e each measurement s e r i e s , t h e c o r e and/or c a n n u l a was c l e a n e d w i t h methanol t o remove f a t and d i r t which c o u l d b u i l d up from h a n d l i n g t h e e l e c t r o d e s . 2.6 E l e c t r i c a l Apparatus D i p o l e Source G e n e r a t o r As p r e s e n t e d i n t h e i n t r o d u c t i o n , an a c t i v e f i b e r can be modeled as a c o n s t a n t c u r r e n t DC d i p o l e s o u r c e t r a v e l l i n g a l o n g t h e f i b e r . In p r a c t i c e , however, a c o n s t a n t AC s o u r c e must be used i n o r d e r t o a c h i e v e a b a l a n c e d c h a r g e - t r a n s f e r i n the d i p o l e . A squarewave was o b s e r v e d t o be u n s u i t a b l e because d u r i n g the " f l a t " p a r t , n o n - l i n e a r p r o c e s s e s o c c u r r e d a t t h e i n t e r f a c e a n d t h e r e c o r d e d s i g n a l was s t r o n g l y d i s t o r t e d . A c c u r a t e a m p l i t u d e measurements were i m p o s s i b l e . A sinewave o f 1 kHz was chosen. The f r e q u e n c y was l a r g e enough so t h a t the same problem d i d not o c c u r as w i t h t h e square wave where the s l o w l y c h a n g i n g a m p l i t u d e r e s u l t e d i n s t r o n g n o n - l i n e a r d i s t o r t i o n s . Higher f r e q u e n c i e s than 1 kHz would have i n c r e a s e d t h e s h u n t i n g ( c f . s e c t i o n 2.4) due t o a f r e q u e n c y dependence o f t h e s p e c i f i c i n t e r f a c e impedance Z^ ( Z ^ can be s i m p l i f i e d as a RC p a r a l l e l c i r c u i t ; ' see f o r example P o l l a k , 1974a). The measurement r e s u l t s i n s e c t i o n 2.4 showed t h a t a t 1 kHz t h e p o t e n t i a l d e c r e a s e due t o s h u n t i n g was a t most 22% f o r r = 48.7 vnn. T h e r e f o r e a sinewave g e n e r a t o r c u r r e n t o f 1 kHz was deemed a p p r o p r i a t e . 45 The C u r r e n t Source The c o n s t a n t c u r r e n t s o u r c e c o n s i s t e d o f two complementary D a r l i n g t o n s T^, T£ / as shown i n Appendix 1, The maximum c o l l e c t o r - e m i t t e r c u r r e n t f o r both p o s i t i v e and n e g a t i v e phase was g i v e n by t h e s t a b i l i z e d s u p p l y v o l t a g e and R 3 / R 3 ' » The c u r r e n t was h e l d c o n s t a n t by c o n t r o l l i n g t h e base c u r r e n t s o f T j / T j ' w i t h t h e op-amps OP^/OP^'. The i n p u t s i g n a l from an •EXACT 123A* VCF f u n c t i o n g e n e r a t o r was f e d t o the op-amps v i a r e s i s t i v e v o l t a g e d i v i d e r s , R2 / R j ' , R 2 ' » The D C - o f f s e t c o n t r o l o f t h e f u n c t i o n g e n e r a t o r a l l o w e d a f i n e adjustment o f the charge b a l a n c e a t t h e e l e c t r o d e - e l e c t r o l y t e i n t e r f a c e . S m a l l d r i f t s i n t h i s b a l a n c e o c c u r r e d over l o n g p e r i o d s o f ti m e , p r o b a b l y due t o some v a r i a t i o n o f t h e s u p p l y v o l t a g e . The imbalance was c o r r e c t e d p e r i o d i c a l l y by hand. No s p e c i a l e f f o r t was made t o keep t h e b a l a n c e e l e c t r o n i c a l l y s t a b l e s i n c e t h e s m a l l DC d r i f t n e i t h e r a f f e c t e d t h e RMS v a l u e of t h e c u r r e n t i n j e c t e d nor t h e RMS v a l u e measured w i t h the v a r i o u s e l e c t r o d e s . The f u n c t i o n g e n e r a t o r p r o d u c e d a v e r y s t a b l e o u t p u t a m p l i t u d e and f r e q u e n c y . The o u t p u t c u r r e n t I Si was p e r i o d i c a l l y measured by means of t h e s m a l l shunt r e s i s t o r 8.2 ft. Through-o u t a l l measurements, I a was 30.5 mA RMS s i n u s o i d a l . T h i s y i e l d e d s u f f i c i e n t l y h i g h a m p l i t u d e s i n the o r d e r o f 1 mV f a r away from the f i b e r ( r » 100 mm) and not t o o l a r g e a m p l i t u d e s up t o about 600 mV a t r = 2.5 mm / 48.7 um. I t s h o u l d be n o t e d t h a t a p o t e n t i a l d i f f e r e n c e o f more t h a n about 100 mV a c r o s s the m e t a l - e l e c t r o l y t e i n t e r f a c e i n f l u e n c e s the s p e c i f i c i n t e r f a c e impedance non-l i n e a r l y , see f o r example P o l l a k (1974a), P l o n s e y (1969). The t r u e p o t e n t i a l d i f f e r e n c e a c r o s s the i n t e r f a c e i s not measurable but s m a l l e r t h a n t h e v o l t a g e measured w i t h the e l e c t r o d e . 46 The two s m a l l s t . s t . beads o f t h e d i p o l e had t o be c l e a n e d from time t o t i m e . The c o n s i d e r a b l e c u r r e n t d e n s i t y o f about 150 mA/cm2 i n d u c e d r e a c t i o n s t h a t l e d t o a b u i l d u p o f r e a c t i o n p r o d u c t s , p r o b a b l y i r o n o x i d e s and/or copper from t h e copper s u l f a t e . The M easuring Set-up Three a s p e c t s were i m p o r t a n t f o r a c c u r a t e measurements; c f . F i g . 2.14: ( i ) As l i t t l e c u r r e n t i a s p o s s i b l e s h o u l d f l o w t h r o u g h t h e e l e c t r o d e a n d a m p l i f i e r t o p r e v e n t l o a d i n g o f t h e p o t e n t i a l s o u r c e V g i n t h e e l e c t r o l y t e . T h i s can be a c h i e v e d by ( Z ^ Z ^ ) >>> R^'. The a v e r a g e d p o t e n t i a l V e a t t h e e l e c t r o d e i s r e p r e s e n t e d as t h e v o l t a g e o f a v o l t a g e d i v i d e r R,/R, ' f e d by t h e volume c o n d u c t o r c u r r e n t i . 3 b b s Rj^/R^' a r e t h e e f f e c t i v e r e s i s t a n c e s o f t h e e l e c t r o l y t e . The c u r r e n t i g t h r o u g h t h e e l e c t r o d e i n t o the a m p l i f i e r must not be m i s t a k e n as t h e s h u n t e d c u r r e n t s when t h e s p e c i f i c i n t e r f a c e impedances Z^ a r e s m a l l , c f . s e c t i o n 2.4. ( i i ) The i n p u t impedance o f the a m p l i f i e r must be much h i g h e r t h a n t h e e l e c t r o d e i m p e d a n c e , Z & >> Z g ( s i m p l i f i e d e q u i v a l e n t e l e c t r o d e i m p e d a n c e Z^; P o l l a k , 1974a). Then o n l y a n e g l i g i b l e v o l t a g e drops over t h e e l e c t r o d e impedance Z g w h i l e t h e f u l l v a l u e o f drops o v e r the a m p l i f i e r impedance Z , where i t i s a m p l i f i e d and measured. ( i i i ) The s i g n a l p a t h o f i g c o n s t i t u t e s a f r e q u e n c y dependent impedance, however s m a l l i i s l The e l e m e n t s C , R s h o u l d be chosen so t h a t e a a th e r o l l - o f f f r e q u e n c i e s a r e o u t s i d e o f t h e f r e q u e n c y band o f i n t e r e s t , i f p o s s i b l e , o r t h a t t h e l i n e a r d i s t o r t i o n s remain m i n i m a l . 47 The t r a n s f e r f u n c t i o n V /V i s g i v e n by -a -e 1 R 1+jojT T = R C G ( = F T R " • 1+535? w h e r e T 6 - R V (2.3) e a a a a T* R +R e a T + a R +R F I g u r e 2 . 1 4 . The e q u i v a l e n t c i r c u i t o f the e l e c t r o l y t e , e l e c t r o d e and a m p l i f i e r Impedances. From P o l l a k (1974b, p. 463) t h e f o l l o w i n g r e a l i s t i c impedance v a l u e s f o r Pt e l e c t r o d e s were assumed ( a t 1 k H z ) : 48 • r e a l e l e c t r o d e w i t h 0.07 mm2 l e a d i n g - o f f s u r f a c e (D = 0.3 mm): = l O ^ f i , - 7 0 ° ; t h i s g a v e R » 300 k i l l |C * 1.5 n F , T » 4.4 x 10" 1* s; e e e • m o d e l e l e c t r o d e w i t h 180 mm2 l e a d i n g - o f f s u r f a c e (D = 7.5 mm) : Z = 40fl, —e -30"; t h i s gave R q « 46ft| ICT « 2 pF, T g « 9 x 1 0 " 5 s. A crude measurement of the model e l e c t r o d e c o n f i r m e d t h e above v a l u e of Z -e « 400., - 3 0 ° . From R e i n e r a Rogoff (1980), an a m p l i f i e r i n p u t impedance Z « 100 MP, || 200 pF — c L ( i n c l u d i n g s h i e l d c a p a c i t a n c e o f c a b l e ) seemed j u s t i f i e d , t o be on t h e c o n s e r v -a t i v e s i d e , f o r a modern measuring system. T h i s gave T » 0.02 s a t 1 kHz. ct Thus f o r th e r e a l e l e c t r o d e , T* « 5 x 10 _ t* s. T h i s means t h a t between the f r e q u e n c i e s 320 Hz and 360 Hz t h e r e i s a s l o p e o f -20 db/decade, c o r r e s p o n d i n g t o an amplitude a t t e n u a t i o n of about -1 dB. O t h e r w i s e , t h e f r e q u e n c y response i s f l a t . T h e r e i s a n a d d i t i o n a l , f r e q u e n c y i n d e p e n d e n t , a t t e n u a t i o n o f R /(R +R ) = 0.997 = -0.026 dB. A h i g h e r a m p l i f i e r i n p u t r e s i s t a n c e o r a lower a e a ^ i n p u t c a p a c i t a n c e would r e s u l t i n a s m a l l e r f r e q u e n c y dependent a t t e n u a t i o n . S p e c i a l t e c h n i q u e s have been d e v e l o p e d by o t h e r s t o r e d u c e t h e i n p u t c a p a c i t a n c e , such as d r i v e n s h i e l d c i r c u i t r y o r a n e g a t i v e i n p u t impedance. The above n u m e r i c a l example f o r a r e a l e l e c t r o d e was g i v e n t o i l l u s t r a t e a p o s s i b l e f r e q u e n c y response of the t r a n s f e r f u n c t i o n G(ju>) i n Eqn. 2.3. Much d i f f e r e n t r e s u l t s a r e o b t a i n e d f o r o t h e r e l e c t r o d e s o r o t h e r a m p l i f i e r s p e c i f i c a t i o n s . F o r the model e l e c t r o d e , no f r e q u e n c y problems o c c u r r e d . With the g i v e n i m p e d a n c e v a l u e s , T* « T q was o b t a i n e d . So t h e r e was no f r e q u e n c y dependence. A l s o , due t o R / ( R +R ) « 0, no o v e r a l l a t t e n u a t i o n o c c u r r e d . T h e r e f o r e , a l l a e a t h r e e p r e v i o u s l y mentioned c o n d i t i o n s ( i ) .. ( i i i ) were s a t i s f i e d . 49 The A m p l i f i e r A d i f f e r e n t i a l a m p l i f i e r w i t h a v e r y h i g h i n p u t impedance and common mode r e j e c t i o n was c o n s t r u c t e d . The c i r c u i t appears i n Appendix 2. I t b a s i c a l l y c o n s i s t e d o f a d i f f e r e n t i a l op-amp OP^ whose i n p u t s were d r i v e n by impedance c o n v e r t i n g FET op-amps OPj/OPj'. Each had an a d j u s t a b l e o f f s e t v o l t a g e w i t h P j / P j ' * T n e r e s i s t o r s R^/R^' compensated f o r t h e i n p u t b i a s c u r r e n t s and w i t h R^ / P 2 t h e g a i n c o u l d be a d j u s t e d f i n e l y ; i t s n ominal v a l u e was s e t t o .5. The o u t p u t v o l t a g e was g i v e n by R 3 + R 3 ' o u t v R^ II P 2 -* *> 2 !•> With Pg the d i f f e r e n t i a l g a i n of O P 2 , which was t h e o r e t i c a l l y one, c o u l d be a d j u s t e d t o a maximum CMR. P r a c t i c a l l y o b t a i n e d v a l u e s o f t h e CMR of t h e complete d i f f e r e n t i a l a m p l i f i e r were i n the o r d e r o f 80 dB. The FET op-amps had an e x t r e m e l y h i g h i n p u t impedance ( s e v e r a l hundred M") and i n p u t c u r r e n t s o f o n l y 10 pA. V _ was m e a s u r e d w i t h a 'FLUKE 8012 A* d i g i t a l m u l t i m e t e r f o r t r u e RMS. o u t ^ F o r t h e v o l t a g e range and f r e q u e n c y used, the a c c u r a c y was ± 0 . 5 % o f r e a d i n g +2 d i g i t s . The t r u e RMS f e a t u r e made i t u n n e c e s s a r y t o b l o c k o f f any DC com-ponents from e l e c t r o d e p o t e n t i a l s o r o f f s e t and temperature d r i f t v o l t a g e s from t h e a m p l i f i e r . v o u t w a s a l s o o b s e r v e d on a 'TEKTRONIX T935 A' o s c i l l o s c o p e . I t m a i n l y s e r v e d as a m o n i t o r i n g i n s t r u m e n t t o d e t e c t any i r r e g u l a r i t i e s i n t h e r e c o r d e d s i g n a l . F i g u r e 2.15 shows a p i c t u r e o f t h e e l e c t r i c a l a p p a r a t u s as used t h r o u g h o u t the i n v e s t i g a t i o n . 50 F i g u r e 2.15. P h o t o g r a p h of the e l e c t r i c a l a p p a r a t u s . M i s c e l l a n e o u s S h i e l d e d c a b l e s were used between the e l e c t r o d e s and t h e a m p l i f i e r i n o r d e r t o reduce n o i s e i n t e r f e r e n c e . S p e c i a l p r e c a u t i o n was o n l y t a k e n as t o remove e l e c t r i c a l equipment from the immediate v i c i n i t y o f the tank and no c o n n e c t i o n was made t o the mains o f equipment o t h e r than n e c e s s a r y . In a d d i t i o n , p r o p e r grounding o f t h e r e f e r e n c e e l e c t r o d e and the s h i e l d s was a b s o l u t e l y n e c e s s a r y . S p e c i a l c a r e had t o be taken t o a v o i d u n d e s i r e d c u r r e n t f l o w t h r o u g h a common ground o f the d i p o l e g e n e r a t o r and the measuring c i r c u i t . T h e r e f o r e t h e 51 p o w e r - s u p p l y f o r t h e two had t o be c o m p l e t e l y i s o l a t e d . F o r c o n v e n i e n c e , t h e g e n e r a t o r s i d e was s e p a r a t e d from t h e mains by a c o n s t a n t v o l t a g e t r a n s f o r m e r . The s k e t c h i n Appendix 3 shows t h e pathways ( d o t t e d l i n e s ) o f t h e unwanted c u r -r e n t s i n the case o f n o n - i s o l a t e d power s u p p l i e s . The c i r c u i t a l s o shows t h a t a common mode v o l t a g e V_ . g e n e r a t e d by t h e d i p o l e , o c c u r r e d a t t h e c o r e and CM ca n n u l a i n the d i f f e r e n t i a l measurement mode. A h i g h CMR o f t h e a m p l i f i e r was t h e r e f o r e e s s e n t i a l . 52 F o r o ut o f o l d e f e l d e s , as men s e i t h , Cometh a l l t h i s newe c o r n from y e r e t o yere} And out o f o l d e bokes, i n good f e i t h , Cometh a l l t h i s newe s c i e n c e t h a t men l e r e . G e o f f r e y Chaucer (The P a r l i a m e n t o f Fowls) I I I . RESULTS AND DISCUSSION 53 3.1 G e n e r a l Remarks For a l l measurements t h r o u g h o u t t h i s i n v e s t i g a t i o n t h e f o l l o w i n g nomenclature was used; see a l s o F i g . 2.2. R e c o r d i n g D i s t a n c e r T h i s was t h e d i s t a n c e between t h e two p a r a l l e l v e r t i c a l p l a n e s t h r o u g h t h e c e n t e r o f the° c o r e and the c e n t e r o f t h e f i b e r , as s k e t c h e d i n F i g . 3.1. The r e c o r d i n g d i s t a n c e was v a r i e d between r = 2.5 .. 100 mm / 48.7 .. 1946 um. F Ipjure 3 . 1 . N o m e n c l a t u r e o f the r e l a t i v e e l e c t r o d e p o s i t i o n . 54 S m a l l e r v a l u e s t h a n r = 2.5 mm / 48.7 ym were deemed t o y i e l d u n r e l i a b l e r e s u l t s due t o a h i g h f i e l d g r a d i e n t . In some cases r e s u l t s were e x t r a p o l a t e d f o r r ••*• 1.285 mm / 25 ym as t h e s m a l l e s t p o s s i b l e r e c o r d i n g d i s t a n c e where t h e l e a d i n g - o f f s u r f a c e was t o u c h i n g the f i b e r o f 50 ym d i a m e t e r . When the c e n t e r o f t h e co r e was v e r t i c a l l y deeper than t h e f i b e r o r when t h e b e v e l was not f a c i n g t h e f i b e r , t h e n t h e s m a l l e s t p o s s i b l e r e c o r d i n g d i s t a n c e was r » 18 mm / 350 ym ( c a n n u l a was t o u c h i n g t h e f i b e r ) . A x i a l D i s t a n c e z T h i s was t h e d i s t a n c e a l o n g t h e f i b e r a x i s , between t h e d i p o l e c e n t e r (= b a s e l i n e i n t e r s e c t i o n o f an AP) and t h e p o i n t t h a t p r o j e c t s p e r p e n d i c u l a r l y t o t h e c e n t e r o f t h e c o r e ; see F i g . 3.1. The a x i a l d i s t a n c e was v a r i e d between z = 0 .. 130 mm / 0 .. 2530 ym. T h i s c o r r e s p o n d e d t o a time span of 632.5 ys a t a p r o p a g a t i o n v e l o c i t y o f 4 m/s. V e r t i c a l D i s t a n c e y T h i s was t h e d i s t a n c e between t h e two h o r i z o n t a l p l a n e s t t h r o u g h t h e f i b e r and t h e c e n t e r o f the c o r e , as shown i n F i g . 3.1. The v e r t i c a l d i s t a n c e was v a r i e d between f o u r d i s t i n c t v a l u e s y = -80 mm / -1557 ym ( c o r e deeper t h a n f i b e r ) , y = 0 ( c o r e and f i b e r i n same h o r i z o n t a l p l a n e ) , y = +80, +160 mm'/ +1557, +3114 ym ( f i b e r deeper than c o r e ) . I n s e r t i o n Depth d The d i s t a n c e between t h e s u r f a c e o f t h e s a l i n e t o t h e t i p of t h e c a n n u l a , as s k e t c h e d i n F i g . 3.2. The i n s e r t i o n depth was v a r i e d between t h r e e d i s t i n c t v a l u e s d = 265, 345, 425 mm / 5157, 6714, 8271 ym. S t a n d a r d i n s e r t i o n depth was d = 345 mm. 55 R e l a t i v e P o s i t i o n o f E l e c t r o d e and F i b e r s The CN e l e c t r o d e was always p o s i t i o n e d so t h a t the b e v e l e d s u r f a c e was p a r a l l e l t o the f i b e r a x i s . Thus t h e f i b e r s were e i t h e r i n f r o n t o r a t t h e back o f a v e r t i c a l p l a n e t h r o u g h t h e c e n t e r o f the c o r e and p a r a l l e l t o t h e f i b e r . F o r r e f e r e n c e , the f i b e r s were d i v i d e d i n t o " f r o n t f i b e r s " and "back f i b e r s " . F i g u r e 3.2 i l l u s t r a t e s t h e s i t u a t i o n . o 9 O o o I o 9 0 9 o o 9 9 O 9 F i g u r e 3 . 2 . F r o n t and back f i b e r s ; i n s e r t i o n d e p t h . 56 The f o l l o w i n g a b b r e v i a t i o n s and c o n v e r s i o n f a c t o r s ( f o r t h e model and r e a l case) o f the AP's were used; c f . a l s o F i g . 1.5. PTPA The peak-to-£eak a m p l i t u d e . The v a l u e s measured were o n l y peak a m p l i t u d e which was h a l f the PTPA f o r a s y m m e t r i c a l AP as g e n e r a t e d by a d i p o l e s o u r c e . The o r d i n a t e i n the p l o t s was c a l i b r a t e d i n u n i t s 1/4ira [dimension m - 1 ] , where I = 0.0305 A ( s e c t i o n 2.6) and o = 1.2 mho/m ( s e c t i o n 2.2). T h i s gave I/4na = 2.0226 x 10 ~ 3 vm. The p l o t s a l s o c o n t a i n t h e c o r r e c t i o n f a c t o r 2 f o r peak amplitude/PTPA. Thus the m u l t i p l i c a t i o n o f the a m p l i t u d e i n th e r e s u l t s w i t h the a p p r o p r i a t e v a l u e of 1/4 TT a ( d e s i r e d I and a) y i e l d t h e t r u e PTPA. PTPD The p_eak-to-peak d u r a t i o n o r r i s e t i m e . The measured v a l u e s were i n mm i n t h e p o s i t i v e z - a x i s , i . e . o n l y h a l f t h e t r u e PTPD. A l l r e s u l t s were c o n v e r t e d from z [mm] t o t h e t r u e PTPD [us] f o r a p r o p a g a t i o n v e l o c i t y o f 4 m/s ( s e c t i o n 1.2/ 1.3). The c o n v e r s i o n f a c t o r was 9.73 us PTPD p e r 1 mm d i s t a n c e z. SD The s p i k e d u r a t i o n . The r e s u l t s i n d i c a t e t h e t r u e SD. The same remarks as f o r t h e PTPD above a p p l y . Key Symbols The key symbols on the c u r v e s do not n e c e s s a r i l y r e p r e s e n t d a t a p o i n t s . The symbols a r e used t o i d e n t i f y the c u r v e s a t "even" a b s c i s s a v a l u e s [um,us]. The measurements were made a t "even" v a l u e s f o r r and z i n the model [mm] . F o r t h e c o n v e r s i o n f a c t o r s , see above. 57 3.2 The W a l l E f f e c t The mechanisms of the w a l l e f f e c t were e x p l a i n e d i n s e c t i o n 2.4. A l s o t h e r e s u l t s f o r t h e w a l l e f f e c t a r i s i n g from the e l l i p t i c a l l e a d i n g - o f f s u r f a c e were p r e s e n t e d and compared ( F i g . 2.6) f o r a "genuine i n s u l a t o r " ( p l e x i g l a s ) and t h e " m e t a l l i c i n s u l a t o r " ( P t ) . I t was seen t h a t due t o t h e f i n i t e s i z e o f t h e a c r y l i c i n s u l a t o r of 7.7 mm x 29.8 mm / 150 ym x 580 ym t h e PTPA was d o u b l e d o n l y where r < 50 ym. The ' w a l l e f f e c t e l e c t r o d e ' d e s c r i b e d i n s e c t i o n 2.5, F i g . 2.10 had a much l a r g e r a r e a o f i n s u l a t i n g w a l l (60 cm 2 o r 2000 times t h e d i a m e t e r o f an SF) s u r r o u n d i n g the 0.8 ram / 15 ym d i a m e t e r s t . s t . l e a d i n g - o f f s u r f a c e . With t h i s e l e c t r o d e the PTPA was d o u b l e d f o r a l l r = 2.5 mm t o 100 mm / 48.7 ym t o 1946 ym. However, f o r AP p o r t i o n s a f t e r t h e peak, the a m p l i t u d e was not q u i t e d o u b l e d . T h i s i m p l i e d t h a t even f o r t h i s v e r y l a r g e i n s u l a t i n g w a l l (compared f o r example t o a SF c o n c e n t r i c n e e d l e , S t a l b e r g & T r o n t e l j , 1979) t h e shape o f t h e AP d i d not remain u n a f f e c t e d by t h e w a l l e f f e c t . E k s t e d t (1964) s t a t e d t h a t t h e w a l l e f f e c t d i d not a l t e r the shape o f the r e c o r d e d s i g n a l but m e r e l y doubled the a m p l i t u d e . The measurements i n t h i s i n v e s t i g a t i o n w i t h b o t h the l a r g e 60 cm 2 w a l l and t h e s m a l l e l l i p t i c 180 mm2 w a l l showed t h a t th e w a l l e f f e c t e x e r t e d by t h o s e f i n i t e s i z e i n s u l a t i n g w a l l s p r o d u c e d a s h o r t e r t h a n t r u e SD due t o a s m a l l e r a m p l i t u d e i n c r e a s e f o r l a t e p o r t i o n s o f t h e AP ( s e c t i o n 3.6). No o t h e r n u m e r i c a l w a l l e f f e c t r e s u l t s were e x t r a c t e d a p a r t from t h o s e a l r e a d y shown i n s e c t i o n 2.4. 3.3 The 'Core' Alone Measurement r e s u l t s of t h e Au p l a t e d ' c o r e ' e l e c t r o d e ( d e s c r i b e d i n s e c -t i o n 2.5) were a l r e a d y p r e s e n t e d i n s e c t i o n 2.4, F i g . 2.6. I t was seen t h a t t h e s i g n a l measured w i t h t h e ' c o r e ' e l e c t r o d e was d i s t o r t e d by s h u n t i n g , 58 " m e t a l l i c w a l l e f f e c t " and a v e r a g i n g . The o v e r a l l e f f e c t was about 50% PTPA a t t e n u a t i o n a t r = 50 um, compared t o the t r u e v a l u e , and l e s s t h a n 10% d e c r e a s e f o r r >350 um. F i g u r e 3.3 shows the a b s o l u t e v a l u e s o f PTPA [ i n u n i t s I/4TTO"] v s . r f o r t h e p o i n t e l e c t r o d e and t h e ' c o r e ' a l o n e . The f i g u r e a l s o e n c l o s e s the two c o r r e s p o n d i n g graphs redrawn from E k s t e d t & S t a l b e r g (1973), where t h e d i p o l e l e n g t h was 2s = 100 um (as opposed t o 2s = 500 pm i n t h i s i n v e s t i g a t i o n ) . As a r e s u l t , t h e d e c l i n e o f t h e PTPA w i t h r was much s t e e p e r due t o a h i g h e r f i e l d g r a d i e n t f o r s m a l l r . E k s t e d t & S t a l b e r g computed the graphs a c c o r d i n g t o Eqn. 1.1. The 'core* p o t e n t i a l was s i m p l y t h e a v e rage o f the p o t e n t i a l s o f a l a r g e number o f p o i n t s w i t h i n t h e 150 um x 580 pm e l l i p s e . U n f o r t u n a t e l y , no r e s u l t s f o r the d i p o l e l e n g t h 2s = 500 pm were a v a i l a b l e so t h a t no d i r e c t comparison o f s i m u l a t e d and p r a c t i c a l l y o b t a i n e d p o t e n t i a l s was p o s s i b l e . The computed r e s u l t s i n F i g . 3.3 were n o r m a l i s e d a t a d a t a p o i n t 480 mV, r = 2.5 mm, c o r r e s p o n d i n g t o PTPA 474.6 m - 1, r = 48.7 pm o f t h e p o i n t e l e c -t r o d e i n F i g . 3.3. I t s h o u l d a g a i n be n o t e d t h a t a c c o r d i n g t o t h e measurements i n t h i s i n v e s t i g a t i o n , t h e p o t e n t i a l a v e r a g i n g i s not t h e o n l y e f f e c t t h a t i s r e s p o n s i b l e f o r the AP d i s t o r t i o n r e c o r d e d w i t h t h e ' c o r e ' e l e c t r o d e . 3.4 The 'Core & I n s u l a t i o n ' Assembly I t c o u l d be e x p e c t e d t h a t t h e w a l l e f f e c t r e s u l t i n g from the e l l i p t i c a l , a n n u l a r epoxy i n s u l a t i o n s u r r o u n d i n g t h e c o r e was a compensatory f a c t o r t h a t c o u n t e r a c t e d the p o t e n t i a l d e c r e a s e caused by the c o r e . As was n o t e d i n s e c -t i o n 2.4, the a n n u l a r , e l l i p t i c a l i n s u l a t i n g w a l l s u r r o u n d i n g t h e c o r e f u r t h e r downplayed the e f f e c t o f s h u n t i n g , due t o t h e enhanced w a l l e f f e c t o f 'core & i n s u l a t i o n ' . F i g u r e 3.4 demonstrates t h a t t h e PTPA of the 'core & i n s u l a t i o n ' e l e c t r o d e l a y between the graphs of the p o i n t and ' c o r e ' e l e c t r o d e f o r r < 175 pm. A t r — 50 pm, about 50% of t h e PTPA de c r e a s e was compensated. At r = 175 59 50 100 150 200 250 300 • 350 400 RECORDING DISTANCE R (MICROMETERS) F 1pure 3 . 3 . The PTPA v s r o f the p o i n t and the ' c o r e ' e l e c t r o d e f o r a d i p o l e l e n g t h o f 2s = 500 „m. A l s o shown a r e the c o r r e s p o n d i n g c u r v e s f o r 2s = 100 „m ( E k s t e d t & S t a l b e r g , 1973) . G e n e r a t e d by a f r o n t SFP (y=0) . 60 F i g u r e 3 . 4 . The PTPA v s r o f the ' c o r e & I n s u l a t i o n ' compared t o the p o i n t and ' c o r e ' e l e c t r o d e ; f r o n t SFP (y=0). 61 ym, t h e compensation was 100%, and f o r even l a r g e r r t h e 'core & i n s u l a t i o n ' assembly r e c o r d e d l a r g e r PTPA's than t h e p o i n t e l e c t r o d e . F i g u r e 3.5 shows the r e l a t i v e PTPA v s . r i n % o f t h e t r u e PTPA, f o r t h e ' c o r e ' and t h e 'core & i n s u l a t i o n ' . The PTPA d e c r e a s e a r i s i n g from t h e ' c o r e ' was c o m p l e t e l y i n e f f e c t i v e a t r > 800 ym. That was where t h e amp l i t u d e i n c r e a s e due t o t h e w a l l e f f e c t o f t h e 'core & i n s u l a t i o n ' r e a c h e d a maximum o f about 140% o f t h e t r u e PTPA. F o r r > 800 ym, the PTPA o f 'core & i n s u l a t i o n ' d e c r e a s e d s t e a d i l y . The s i z e o f the e l l i p t i c a l , a n n u l a r epoxy i n s u l a t i o n s u r r o u n d i n g t h e c o r e was no t l a r g e enough t o e x e r t t h e f u l l w a l l e f f e c t f o r a l l r e c o r d i n g d i s t a n c e s r . A t r = 800 um t h e f a c t o r was 1.4 and d e c r e a s e d t o 1.25 a t r = 1800 ym. The d o t t e d l i n e i n F i g . 3.5 i s an e s t i m a t e d graph o f t h e PTPA f o r 'core & i n s u l a t i o n ' i n t h e case o f a v e r y s m a l l l e a d i n g - o f f s u r f a c e where no p o t e n t i a l a v e r a g i n g t a k e s p l a c e . The d o t t e d graph would e v e n t u a l l y l e a d t o t h e o r d i n a t e v a l u e o f 200% a t s m a l l e r r ( f u l l w a l l e f f e c t , f a c t o r 2 ) . 3.5 The Complete C o n c e n t r i c Needle E l e c t r o d e When c o r e , i n s u l a t i o n and c a n n u l a were a l l assembled, t h r e e d i f f e r e n t s i g n a l s c o u l d be p i c k e d up: ( i ) t h e c o r e p o t e n t i a l w . r . t . t h e remote e l e c t r o d e , o r 'core v s . remote'; ( i i ) t h e c a n n u l a p o t e n t i a l w .r.t. t h e remote e l e c t r o d e , o r 'cannula v s . remote'; ( i i i ) the co r e p o t e n t i a l w . r . t . t h e c a n n u l a p o t e n t i a l as measured d i f f e r e n -t i a l l y , o r 'core v s . c a n n u l a ' . In o r d e r t o check- f o r measurement e r r o r s , a l l c a s e s ( i ) .. ( i i i ) were r e c o r d e d and t h e measured v a l u e s 'core v s . c a n n u l a ' compared w i t h t h e m a t h e m a t i c a l l y o b t a i n e d d i f f e r e n c e o f the measured v a l u e s 'core v s . remote' and 'cann u l a v s . remote'. The measured and t h e computed case ( i i i ) d i f f e r e d by a t most 10%, 62 F i g u r e 3 . 5 . The PTPA i n °/„ o f the t r u e PTPA v s r o f the ' c o r e ' and ' c o r e & i n s u l a t i o n ' e l e c t r o d e ; f r o n t SFP (y=0) . 63 i n d i c a t i n g t h a t t h e e l e c t r o l y t i c tank model as w e l l as t h e e l e c t r i c a l a p p a r a t u s s u p p l i e d r e l i a b l e r e s u l t s . F o r t h e s i m u l a t e d MUP (see s e c t i o n 3.9) an a r i t h m e -t i c mean v a l u e of the measured and computed 'core v s . c a n n u l a ' p o t e n t i a l s was t a k e n as the e v a l u a t i o n b a s i s . The comparison o f th e 'core v s . remote* p o t e n t i a l and t h e p o t e n t i a l s measured w i t h the s u b - a s s e m b l i e s 'core & i n s u l a t i o n ' and ' c o r e ' shed l i g h t onto t h e i n d i v i d u a l e f f e c t s o f the epoxy i n s u l a t i o n and t h e c a n n u l a . On t h e o t h e r hand, the comparison of th e d i f f e r e n t i a l s i g n a l 'core v s . c a n n u l a ' ( t h e r e g u l a r r e c o r d i n g c o n f i g u r a t i o n of t h e CNE) w i t h t h e " i d e a l " p o i n t e l e c t r o d e measure-ments y i e l d e d new e v i d e n c e o f t h e p r o p e r t i e s and s i g n a l d i s t o r t i o n s o f the CNE as a whole. Tog e t h e r w i t h t h e knowledge of t h e causes o f i t s s h o r t c o m i n g s , new ways were sought t o improve the p r o p e r t i e s o f the CNE. Those m a t t e r s a r e d i s -c u s s e d i n s e c t i o n 3.10. 3.6 S i n g l e F i b e r P o t e n t i a l Measurements Peak-to-Peak Amplitude F i g u r e 3.6 shows t h e PTPA v s . r i n % o f t h e t r u e PTPA, f o r t h e c a s e s 'core vs. remote' and 'core v s . c a n n u l a ' measured w i t h t h e complete CN e l e c t r o d e assembly from a f r o n t f i b e r . The graphs o f the ' c o r e ' and 'core & i n s u l a t i o n ' e l e c t r o d e a r e a l s o drawn f o r comparison. I t can be seen t h a t f o r r < 200 um t h e PTPA was v e r y s i m i l a r f o r 'core & i n s u l a t i o n * , 'core v s . remote' and 'core vs. c a n n u l a ' , i n d i c a t i n g a minor c a n n u l a e f f e c t . When r became l a r g e r , how-e v e r , obvious e f f e c t s o f the c a n n u l a p r e s e n c e o c c u r r e d . Even when the c a n n u l a p o t e n t i a l was not s u b t r a c t e d e l e c t r i c a l l y , t h e PTPA was d r a s t i c a l l y r e d u c e d compared t o the case 'core & i n s u l a t i o n * . F o r r > 1200 um (where t h e r e was no l o n g e r any p o t e n t i a l d e c r e a s e due t o the e f f e c t s a t t h e c o r e ; s e c t i o n 2.4) the PTPA dropped below the t r u e v a l u e p r e s e n t i n the volume c o n d u c t o r . T h i s p o t e n -p o i n t e l e c t r o d e « t r u e P T P A = 100% v ' c o r e ' o ' c o r e & i n s u l a t i o n ' • c o m p l e t e CNE ( ' c o r e v s r e m o t e ' ) • c o m p l e t e CNE ( ' c o r e v s c a n n u l a ' ) 400 600 800 1000 1200 1400 1600 1800 RECORDING DISTANCE R (MICROMETERS! The PTPA 1n % o f the t r u e PTPA vs r o f the c o m p l e t e CNE ( ' c o r e vs r e m o t e ' , ' c o r e v s c a n n u l a ' ) , compared t o the ' c o r e ' and ' c o r e & I n s u l a t i o n ' e l e c t r o d e ; f r o n t SFP (y=0) . 65 p o t e n t i a l d e c r e a s e c o u l d o n l y be a t t r i b u t e d t o a f i e l d d i s t o r t i o n by t h e mere pr e s e n c e o f the c a n n u l a . I n t h e d i f f e r e n t i a l mode/ the c a n n u l a p i c k e d up a c o n s i d e r a b l e s i g n a l which lowered the PTPA of t h e 'core v s . c a n n u l a ' c o n f i g u r a -t i o n even more (see a l s o s e c t i o n s 3.7, 3.9). , When the a c t i v e f i b e r was a t t h e back o f t h e e l e c t r o d e b e v e l , a massive s h i e l d i n g was e x e r t e d by t h e c a n n u l a . F i g u r e 3.7 d i s p l a y s t h e pr o n o u n c e d d i r e c t i o n a l p r o p e r t y o f the CN e l e c t r o d e . Shown a r e t h e graphs o f t h e PTPA i n % o f t h e t r u e v a l u e , f o r t h e s i g n a l s 'core v s . remote' and 'cannula v s . remote', r e c o r d e d from a back SFP. I t i s seen t h a t t h e s i g n a l from a back f i b e r p i c k e d up by the 'core v s . remote' was o n l y between 10% t o 40% of t h e t r u e v a l u e . A f r o n t f i b e r p r o d u c e d between 70% and 115% o f t h e t r u e v a l u e . The c a n n u l a s i g n a l a r i s i n g from a back f i b e r ( a t y = 0) was even l a r g e r t h a n t h e c o r e s i g n a l 1 T h e r e f o r e t h e d i f f e r e n t i a l s i g n a l 'core v s . c a n n u l a ' was n e g a t i v e ( d o t t e d g r a p h ) . F o r comparison, the c a n n u l a PTPA from a f r o n t f i b e r was a l s o p l o t t e d , which was much s m a l l e r than from a back f i b e r . Back f i b e r s were c l o s e t o a l a r g e p o r t i o n o f t h e c a n n u l a b u t more d i s t a n t from the c o r e . F r o n t f i b e r s , however, "saw" o n l y t h e e l l i p t i c , a n n u l a r p a r t o f t h e c a n n u l a b u t the f u l l a s p e c t o f the e l l i p t i c c o r e . D r a s t i c d i f f e r e n c e s i n t h e PTPA between s i g n a l s from f r o n t and back f i b e r s were a l s o r e c o r d e d f o r v a l u e s o f y * 0. No s e p a r a t e r e s u l t s a r e shown here which a r e i m p l i c i t l y c o n t a i n e d i n t h e MUP c u r v e s ( s e c t i o n 3.9). Peak-to-peak D u r a t i o n F i g u r e 3.8 p r e s e n t s the PTPD v s . r f o r t h e v a r i o u s e l e c t r o d e s . The d o t t e d g r a p h i s t h e f u n c t i o n PTPD = r/2/(4m/s), i n c l u d i n g a l l c o n v e r s i o n f a c t o r s (see s e c t i o n 3.1). A c c o r d i n g t o George (1970), the asymptote o f t h e l o c u s o f 9<f>^ /3z 66 120 -i ] io A 100 cr CL 10 A 60 poin t e l e c t r o d e » t rue PTPA » 100% ' c o r e vs remote ' , f ront • ' c o r e vs remote ' , back a 'cannula vs remote ' , f ront * ' cannula vs remote ' , back o ' core vs c a n n u l a ' , f ront • ' c o r e vs c a n n u l a ' , back (negat ive! ) 50 A 40 A 30 A 20 A 10 A i • • • i • • .• i • i > ' • i • • i i • i • | 200 400 600 800 1000 ]200 1400 1600 1800 RECORDING DISTANCE R(MICROMETERS) F i g u r e 3 .7 The PTPA In % o f the t r u e PTPA vs r o f the c o m p l e t e CNE ( ' c o r e v s r e m o t e ' , ' c a n n u l a v s r e m o t e ' , ' c o r e v s c a n n u l a ' ) ; f r o n t and back SFP (y=0) . F i g u r e 3 , 8 . The PTPD v s r o f the p o i n t , ' c o r e ' , ' c o r e & I n s u l a t i o n ' e l e c t r o d e and the c o m p l e t e CNE ( ' c o r e v s r e m o t e ' , ' c a n n u l a vs r e m o t e ' , ' c o r e vs c a n n u l a ' ) , compared t o the a s y m p t o t e o f the l o c u s O f o r the t h e o r e t i c a l PTPD ( a c c o r d i n g to G e o r g e , " J 1970) ; f r o n t SFP (y=0) . 68 = 0 ( d i f f e r e n t i a t e d Eqn. 1.1) i s given by z = r//2. Where z » s, the PTPD should coincide with the asymptote. Due to the potential distribution devia-tions in the tank for large r (cf. section 2.3) the measured curve never quite reached the asymptote. For points z + s close to the dipole, the PTPD equals 2s/(propagation velocity). This was found to be true for the point, 'core' and 'core & insulation" electrodes which a l l shared the same curve as seen in Fig. 3.8. The shortest PTPD of 125 us for r + 25 ym was directly dependent on the dipole length 2s = 500 ym. Since the PTPD vs. r was the same for point, 'core' and 'core & insulation* electrode, i t was concluded that neither shunt-ing nor wall effect nor averaging influenced the PTPD measurably. In con-trast, the presence of the cannula produced a shorter PTPD of the 'core vs. remote' signal for r > 200 ym. A slope of 72/4 was also established for r > 1200 ym with a constant difference of about -60 ys. The PTPD of the 'cannula vs. remote' signal was very long. It was on average about 200 ys longer than when picked up with the point electrode. An approximate slope of /i/4 was maintained for a l l r. The long PTPD of the cannula signal was responsible for the short PTPD's measured differentially 'core vs. cannula'. The slope of /2/4 was reached for r > 1600 ym with a constant difference of about -180 ys compared to the true value. Figure 3.9 illustrates the differing PTPD's for front and back SFP's. The highly asymmetrical beveled t i p of the electrode influenced the shape of the recorded SFP's significantly. It can be seen that a back fiber produced a very much longer PTPD recorded with the 'core vs. remote' and a shorter PTPD record-ed with the 'cannula vs. remote', both compared to a front fiber. The result was a shorter PTPD recorded differentially 'core vs. cannula' from a back fiber than when picked up from a front fiber. PTPD's for values of y * 0 are impli-c i t l y contained in the results of MUP's (section 3.9). A F i g u r e 3 . 9 . The PTPD v s r o f the c o m p l e t e CNE ( ' c o r e vs r e m o t e ' , ' c a n n u l a v s r e m o t e ' , ' c o r e vs c a n n u l a ' ) ; f r o n t and back SFP (y=0 ) . 6 7 0 Spike D u r a t i o n The SD was somewhat r e l a t e d t o t h e PTPD. The graphs f o r t h e SD v s . r i n P i g . 3.10 e x h i b i t e d t h e same tendency as t h e graphs f o r t h e PTPD v s . r i n F i g . 3.8. The SD of the s i g n a l s r e c o r d e d w i t h the p o i n t and t h e 'core* e l e c t r o d e was e s s e n t i a l l y t h e same f o r a l l r . The 'core & i n s u l a t i o n ' r e c o r d e d a 50 us s h o r t e r SD where r > 500 ym. T h i s was due t o a v a r y i n g w a l l e f f e c t f a c t o r a l o n g z, as a l r e a d y mentioned i n s e c t i o n 3.2. F o r s m a l l r , t h e SD t e n d e d t o become s l i g h t l y l o n g e r t h a n the t r u e v a l u e . The d i f f e r e n c e s were s m a l l e r t h a n 100 ys f o r r •*• 25 ym. T h i s was m a i n l y due t o t h e PTPA d e c r e a s e o f about 30% f o r s m a l l r , i n a l l cases 'core & i n s u l a t i o n ' , 'core v s . remote' and 'core v s . c a n n u l a ' ( F i g s . 3.5, 3.6). The s h o r t e s t SD was o b t a i n e d w i t h 'core v s . c a n n u l a ' due t o a v e r y l o n g SD o f t h e 'core v s . remote' s i g n a l . The e l e c t r i c a l l y n o t c o n n e c t e d b u t p h y s i c a l l y p r e s e n t c a n n u l a a l o n e c a u s e d a s h o r t e r than t r u e SD. F i g u r e 3.11 compares the SD's a r i s i n g from f r o n t and back f i b e r s . A g a i n , t h e tendency was v e r y s i m i l a r t o the PTPD ( F i g . 3.9). Both, t h e s h o r t e n e d SD and t h e PTPD o f back f i b e r s f u r t h e r a c c e n t u a t e d t h e d i r e c t i o n a l p r o p e r t y o f t h e CNE. The r e s u l t s o f the SD f o r v a l u e s o f y * 0 from f r o n t and back f i b e r s a r e i m p l i c i t l y c o n t a i n e d i n t h e MUP's; c f . s e c t i o n 3.9. 3.7 E f f e c t o f D i f f e r e n t Cannula I n s e r t i o n Depths I t was shown by P o l l a k (1971) t h a t t h e c a n n u l a p o t e n t i a l d e c r e a s e d w i t h t h e i n s e r t i o n depth i n t o t h e t i s s u e . The average o f t h e p o t e n t i a l s i n t h e volume c o n d u c t o r a l o n g t h e s u r f a c e o f t h e c a n n u l a becomes s m a l l e r when more s u r f a c e a r e a i s exposed t o t h e t i s s u e . P o l l a k d e v e l o p e d t h e f o l l o w i n g e x p r e s s i o n f o r the c a n n u l a p o t e n t i a l V r V * V ( r ) • ; where X » r (3.1) C O A O 71 1400 -, 1300 if) a o c_> UJ C/) o or a 1200 1100 rr 1000 900 4 5 800 4 700 600 4 500 4 400 300 • point electrode o 'core' o 'core & insulation' •complete CNE ( ' c o r e vs remote') A complete CNE ('cannula vs remote') •complete CNE ('core vs cannula') 2 0 0 ' I ' r ~ 1 ' I 1 — ' — ' — 1 | ' — i — ' — i — j — r — i — i — i — | — i — i — i — i — | — i — i , i — | — r -100 200 300 400 5 0 0 600 700 RECORDING D ISTANCE R (MICROMETERS] 800 F i g u r e 3 . 1 0 , The SD vs r o f the p o i n t , ' c o r e ' , ' c o r e & In -s u l a t i o n ' e l e c t r o d e and the c o m p l e t e CNE ( ' c o r e v s r e m o t e ' , ' c a n n u l a v s r e m o t e ' , ' c o r e v s c a n n u l a ' ) ; f r o n t SFP (y=0) . 72 a a R E C O R D I N G D I S T A N C E R ( M I C R O M E T E R S ) F i g u r e 3 . 1 1 . The SD vs r o f the c o m p l e t e CNE ( ' c o r e vs r e m o t e ' , ' c a n n u l a vs r e m o t e ' , ' c o r e v s c a n n u l a ' ) ; f r o n t and back SFP (y=0) . 73 X i s the length of the cannula in contact with the tissue (corresponding to d) and r Q the recording distance r as defined in section 3.1. Equation 3.1 is only valid i f the specific interface impedance between cannula and tissue i s much larger than the bulk r e s i s t i v i t y of the electrolyte (no shunting of the volume conductor currents; see section 2.4). In addition, Eqn. 3.1 was developed for a front SFP at y = 0. Figure 3.12 presents the graphs of the cannula PTPA vs. r for three inser-tion depths d = 265 .. 425 mm / 5157 .. 8217 um. As expected, a decreased cannula potential resulted for deeper insertion. The graphs according to Eqn. 3.1 were also drawn for comparison*. Pollak*s estimate of V c was reasonably good where r > 20 mm / 38.9 um. For r < 20 mm, however, Eqn. 3.1 underesti-mated V . It should be noted that not only the ratio of cannula and core PTPA c J alone was an important aspect for the distortion of the differential signal, but also the PTPD and SD of the cannula potential. Equation 3.1 did not supply the latter information and could therefore only be used as a rough estimate of the cannula potential and i t s dependence on the insertion depth for a SFP. Figure 3.13 shows the results of the cannula PTPA vs. r for different insertion depths, where y = ±80 mm / ±1557 um. Due to mechanical limitations (cf. sections 2.2, 3.1) i t was not possible to take the same two insertion depths d for both values of y. However, the difference of insertion depth was identical in both cases, namely Ad = 80 ram / 1557 ym. It i s evident that when y * 0 the cannula potential underwent smaller changes for varying insertion depths than when y = 0. It can also be seen that for r < 600 ym the absolute For V(r Q) the PTPA's recorded with the point electrode were taken (Fig. 3.3). 74 F 1 q u r e 3 . 1 2 . The c a n n u l a PTPA v s r f o r d i f f e r e n t I n s e r t i o n d e p t h s d . A l s o shown a r e t h e c u r v e s o f E q n . 3.1 ( P o l l a k , 1971) ; f r o n t SFP (y=0 ) . 500 - i I -• • • i • • • i • • • i i .. i | i , 0 200 400 600 800 1000 1200 1400 1600 1800 RECORDING DISTANCE R (MICROMETERS) F 1 q u r e 3 , 1 3 . The c a n n u l a PTPA v s r f o r d i f f e r e n t i n s e r t i o n d e p t h s d ; f r o n t SFP ( y * 0 ) . 76 c a n n u l a PTPA was l a r g e r a t y = +1557 um and s m a l l e r f o r a l l r a t y = -1557 um than i n the case y = 0 ( F i g . 3.12). S e c t i o n 3.9 t r e a t s t h e a s p e c t s o f t h e c a n n u l a p o t e n t i a l i n more d e t a i l i n c o n n e c t i o n w i t h MU's. F i g u r e 3.14 compares a l l cases y = -1557, 0, +1557 um i n a r e l a t i v e manner where the c a n n u l a p o t e n t i a l i s p l o t t e d i n % o f the 'core v s . remote' PTPA, as a f u n c t i o n o f the r e c o r d i n g d i s t a n c e r . I t i s seen t h a t i n the case y = 0 and r < 100 um the c a n n u l a p o t e n t i a l never exceeded 1% o f the c o r e PTPA even f o r the s m a l l e s t i n s e r t i o n depth t e s t e d (d = 5157 ym). The c a n n u l a p o t e n t i a l r e a c h e d 25% (d = 8271 ym) t o 45% (d = 5157 ym) a t r = 1600 ym. T h i s demonstrates t h a t f o r l a r g e r r e c o r d i n g d i s t a n c e s a s m a l l e r i n s e r t i o n depth c o u l d e n t a i l a c a n n u l a p o t e n t i a l o f a l m o s t h a l f the c o r e p o t e n t i a l . F o r f i b e r s a t y # 0, d i f f e r i n g i n s e r t i o n depths d i d not a l t e r t h e c a n n u l a p o t e n t i a l more t h a n 5% t o 10%. The c a n n u l a p o t e n t i a l was between 40% and 60% o f t h e c o r e p o t e n t i a l f o r y = -1557 ym and 80% t o w e l l over 100% f o r y = +1557 ym. Thus the l o c a t i o n o f t h e f i b e r was o f g r e a t e r i n f l u e n c e on the c a n n u l a p o t e n t i a l t h a n t h e i n s e r t i o n d e p t h . I t s h o u l d a l s o be emphasized t h a t t h e r e l a t i v e c o n t r i b u t i o n o f t h e c a n n u l a p o t e n -t i a l t o the c o r e p o t e n t i a l i s more i m p o r t a n t than t h e c a n n u l a p o t e n t i a l i t s e l f . E q u a t i o n 3.1 o n l y s u p p l i e s a rough e s t i m a t e of t h e c a n n u l a p o t e n t i a l f o r a f r o n t SFP a t y = 0. In r e a l i t y , however, a s i n g l e f i b e r i s never a c t i v e a l o n e b u t always a t l e a s t a whole MU. The f o r m u l a i n Eqn. 3.1 i s i n a d e q u a t e when a p p l i e d t o motor u n i t r e c o r d i n g . The c a n n u l a p o t e n t i a l s o f a MU a r e t r e a t e d i n s e c t i o n 3.9. 77 RECORDING DISTANCE R(MICROMETERS) F Igure 3 . 1 4 . The c a n n u l a p o t e n t i a l i n % o f the c o r e PTPA v s r f o r v a r i o u s v a l u e s o f d and y ; f r o n t S F P . 78 . 3.8 The Motor U n i t Model The SFP d i s c u s s e d so f a r made i t p o s s i b l e t o a s s e s s t h e e f f e c t s of p o t e n -t i a l a v e r a g i n g , i n s u l a t i n g w a l l , f r o n t and back f i b e r s , v a r y i n g v a l u e s o f y and d. Y e t p r a c t i c a l l y , t h e CN e l e c t r o d e i s almost never used f o r s i n g l e f i b e r EMG f o r r e a s o n s which were e x p l a i n e d i n s e c t i o n 1.6. Many i n v e s t i g a t i o n s f u r n i s h e d i n f o r m a t i o n on t h e s t r u c t u r e o f a MU. B u c h t h a l e t a l . (1957, 1973) r e p o r t e d t h a t t h e t e r r i t o r y o f one motor u n i t i n t h e normal human b i c e p s b r a c h i i muscle was n e a r l y c i r c u l a r w i t h a mean di a m e t e r o f 5 mm. C h r i s t e n s e n (1959) e s t i m a t e d t h e average number o f f i b e r s i n one MU o f t h a t muscle as 163. S t a l b e r g & Gath ( i n p r e s s ) o b t a i n e d an e s t i m a t e of a t l e a s t 200 f i b e r s . The f i b e r arrangement was r e p o r t e d t o be u n i f o r m l y randomly s c a t t e r e d over the t e r r i t o r y ( B r a n d s t a t e r & Lambert, 1973; S t a l b e r g e t a l . , 1976). The r e s u l t i n g f i b e r d e n s i t y o f 163 f i b e r s / 19.6 mm2 = 8.3 f i b e r s / mm2 l i e s w i t h i n the range o b s e r v e d by S t a l b e r g (1980) (1.35 f i b e r s / 300 um uptake r a d i u s = 9.5 f i b e r s / mm2) and T h i e l e & Boehle (1975) (average 5 f i b e r s / 700 um uptake r a d i u s = 6.5 f i b e r s / mm 2). The uptake o r p i c k u p r a d i u s i s d e f i n e d ( S t a l b e r g & T r o n t e l j , 1979) as t h e r e c o r d i n g d i s t a n c e r where the PTPA drops t o 5% o f the v a l u e r e c o r d e d a t t h e f i b e r ( r « 25 pra i n t h i s i n v e s t i g a -t i o n ; c f . s e c t i o n 3.1). Under the assumption of an e x t e n s i v e homogenous volume c o n d u c t o r , the MUP i s t h e s u p e r p o s i t i o n of a l l i n d i v i d u a l SFP's b e l o n g i n g t o t h e MU ( H e l m h o l t z ' P r i n c i p l e , 1853). The a mplitude and shape o f the MUP i s v e r y much dependent on the l o c a t i o n of the l e a d i n g - o f f s u r f a c e w i t h i n the MU. I t would have been d i f f i c u l t t o r e p r e s e n t a random s c a t t e r o f f i b e r s i n t h e e l e c t r o l y t i c tank model. F i g u r e 3.15 d e p i c t s t h e s i m p l i f i e d s p a t i a l arrangement of f i b e r s t h a t was chosen t o model a MU. I t c o n s i s t e d o f a 'back-ground' a r r a y w i t h f i v e f r o n t and back f i b e r s each a t r = 20, 40, 60, 80, 100 79 o o o o o u • 160 mm o o o o o ij ' £0 mm frma 'backijnmi' o <j-0 t • - SO n o o • < J n*ar«t fibers o o o o o o o o o o back 'background' o o o o o I o o o o o o o o o o o F j g u r e 3 , 1 5 . The motor u n i t model f i b e r a r rangement w i t h 41 ' b a c k g r o u n d ' f i b e r s and 1 n e a r e s t f i b e r a t r = 2 . 5 , 5. 10 o r 20 mm / 4 8 . 7 . 9 7 . 3 , 195 o r 389 j,m. mm / 389, 778, 1168, 1557, 1946 um a t t h e f o u r l e v e l s y = 160, 80 0, -80 mm / 3114, 1557, 0, -1557 um. Another 'background' f i b e r was assumed a t r = 0, y = -80 mm ( j u s t below the c a n n u l a t i p ) . Thus t h e 'background' a r r a y c o n t a i n e d 41 f i b e r s . In o r d e r t o s i m u l a t e f o u r d i f f e r e n t MUP's ( c o r r e s p o n d i n g t o f o u r pseudo-random e l e c t r o d e p o s i t i o n s ) one a d d i t i o n a l f i b e r was p l a c e d a t y = 0, r = 2.5 mm / 48.7 o r 5 mm / 97.3 um o r 10 mm / 195 um. Thus t h r e e MUP's were composed o f the 41 f i x e d 'background' f i b e r s p l u s t h e one f i b e r v e r y c l o s e t o th e l e a d i n g - o f f s u r f a c e ( r e c o r d i n g d i s t a n c e s as a b o v e ) . The f o u r t h MUP s i m p l y 80 c o n s i s t e d of the 41 'background' f i b e r s ( i . e . t h e c l o s e s t f i b e r was a t r = 20 mm / 389 um). That s o l u t i o n of MU r e p r e s e n t a t i o n was deemed s u i t a b l e t o a s s e s s t h e t e n d e n c i e s o f the CNE b e h a v i o u r . In a volume c o n d u c t o r , more d i s t a n t f i b e r s do not c o n t r i b u t e t o the s p i k e o f the MUP. A v a r y i n g arrangement o f the d i s t a n t f i b e r s does not a f f e c t t h e i r c o n t r i b u t i o n t o the MUP v e r y much. T h e r e -f o r e t h e model 'background' f i b e r a r r a y was k e p t i n a f i x e d arrangement. Only t h e d i s t a n c e s o f the c l o s e s t f i b e r s , which i n a volume c o n d u c t o r i n f l u e n c e m a i n l y the PTPA and PTPD of the MUP, were made v a r i a b l e . Thus the f o u r d i f -f e r e n t MU arrangements modeled the case where i n c l i n i c a l EMG t h e CN e l e c t r o d e were moved s l i g h t l y i n t h e muscle so t h a t o n l y the f i b e r s c l o s e s t t o the l e a d i n g - o f f s u r f a c e changed t h e i r r e c o r d i n g d i s t a n c e s w h i l e t h e more d i s t a n t f i b e r s p r e s e r v e d t h e i r r e l a t i v e p o s i t i o n . The MU model i n F i g . 3.15 r e p r e s e n t e d a f i b e r d e n s i t y ('FD*; S t a l b e r g & T r o n t e l j , 1979) of about 2.2 f i b e r s / mm2 when a l l 41 f i b e r s were e n c l o s e d , o r about 2.9 f i b e r s / mm2 when o n l y the seven n e a r e s t f i b e r s i n t h e v i c i n i t y o f t h e l e a d i n g - o f f s u r f a c e were c o n s i d e r e d . The FD i n t h e MU model was k e p t lower than the r e p o r t e d FD's (see p r e c e d i n g p a r a g r a p h s ) f o r t h r e e r e a s o n s : ( i ) The e f f e c t s of the f u l l MU ( w i t h i n the uptake area) would be under-e s t i m a t e d w i t h a low FD. T h i e l e & B o ehle (1975) r e p o r t e d 2 t o 12 f i b e r s (mean 5) c o n t r i b u t i n g t o the MUP w i t h i n an uptake r a d i u s of 0.7 mm. T h i s y i e l d e d a FD between 2.6 and 15.6 f i b e r s / mm2. T h e r e -f o r e the model FD o f 2 t o 3 f i b e r s / mm2 r e p r e s e n t e d a "worst c a s e " s i t u a t i o n . ( i i ) The low FD MU arrangement i n F i g . 3.15 made i t e a s i e r t o s e p a r a t e the e f f e c t s o f f r o n t f i b e r s and back f i b e r s . ( i i i ) To m i n i m i z e the number o f computations r e q u i r e d . 81 MUP's were o b t a i n e d from t h e s u p e r p o s i t i o n o f t h e d a t a p o i n t s . In t h e r e s u l t s , o n l y the r e c o r d i n g d i s t a n c e r o f the n e a r e s t f i b e r s (2.5 t o 20 mm / 48.7 t o 389 ym) i s i n d i c a t e d . So, f o r example, r = 10 mm / 195 ym r e p r e s e n t s t h e case o f one f i b e r a t r = 10 mm p l u s 41 'background' f i b e r s , w h i l e r = 20 mm s i m p l y r e f e r s t o t h e 'background' a r r a y a l o n e . F o r comparisons w i t h SFP's, r i s t h e r e c o r d i n g d i s t a n c e o f t h e n e a r e s t f i b e r w i t h o u t t h e 'background' a r r a y . S t a n d a r d i n s e r t i o n depth was d = 345 mm / 6714 ym, e x c e p t f o r y = 160 mm / 3114 ym where d = 425 mm / 8271 ym due t o m e c h a n i c a l l i m i t a t i o n s ( c f . s e c t i o n s 2.2, 3.1). 3.9 Motor U n i t P o t e n t i a l Measurements Cannula P o t e n t i a l F i g u r e 3.16 d i s p l a y s t h e r a t i o i n % o f c a n n u l a / c o r e p o t e n t i a l as a f u n c -t i o n o f z, w i t h r as parameter. The p l o t s o f SFP and MUP r e v e a l s t r i k i n g d i f -f e r e n c e s . At the v a l u e o f z where the peak a m p l i t u d e o c c u r r e d on t h e c o r e s i g n a l ( d o t t e d "peak" l i n e ; c o r r e s p o n d i n g t o h a l f t h e PTPD) t h e c a n n u l a p o t e n -t i a l a r i s i n g from a SF was 0.5% t o 4.3% ( r = 2.5 t o 20 mm / 48.7 t o 389 ym) o f the c o r e PTPA. The c o r r e s p o n d i n g v a l u e s from a MUP were 10% t o 66%. These p e r c e n t a g e s compared w e l l t o t h e 25% t o 30% r e p o r t e d by B u c h t h a l (1954). F o r l a t e p o r t i o n s o f the r e c o r d e d p o t e n t i a l a t z = 500 ys from the b a s e l i n e i n t e r -s e c t i o n , the c a n n u l a p i c k e d up 52% t o 57% o f the SFP and 84% t o 87% o f t h e MUP ( a l l r ) . The l a r g e c a n n u l a p o t e n t i a l a r i s i n g from the MU was e x p l i c a b l e by t h e f a c t t h a t many f i b e r s were c l o s e t o the c a n n u l a b u t f a r from t h e c o r e . F i g u r e 3.14 i n s e c t i o n 3.7 i l l u s t r a t e d t h a t a SF a t y = +80 mm / +1557 ym p r o d u c e d a ca n n u l a p o t e n t i a l t h a t was l a r g e r t h a n the c o r e p o t e n t i a l when r < 800 ym. 82 1 0 0 N Q_ I A X I S (MICROSECONDS) F j g u r e 3 . 1 6 . The c a n n u l a p o t e n t i a l In % of the c o r e p o t e n t i a l v s z f o r v a r i o u s v a l u e s o f r; f r o n t SFP (y=0) and MUP. 83 Peak-to-Peak Amplitude The PTPA r e c o r d e d w i t h 'core v s . remote' and 'cannula v s . remote' from t h e MO was e x p e c t e d t o be l a r g e r t h a n from the SF, f o r a l l r . T h a t was c o n f i r m e d as F i g . 3.17 shows. I t i s most i n t e r e s t i n g t o see t h a t a t r = 340 um t h e d i f -f e r e n t i a l s i g n a l 'core v s . c a n n u l a ' o f t h e MUP became s m a l l e r t h a n t h e one of t h e SFP. T h i s was due t o a g r e a t l y i n c r e a s e d c a n n u l a p o t e n t i a l which remained p r a c t i c a l l y c o n s t a n t f o r a l l r . The MUP graph o f 'core v s . c a n n u l a ' i n d i c a t e s t h a t t h e uptake r a d i u s of the CN e l e c t r o d e was about 400 um. The v a l u e was o b t a i n e d by e x t r a p o l a t i n g the PTPA from r = 50 um t o r •*• 25 um ( d o t t e d graph, n o t measured; see remark i n s e c t i o n 3.1). S t a l b e r g (1980) and T h i e l e & Boehle (1975) r e p o r t e d a CNE p i c k u p r a d i u s of 700 ym t o 1 mm. The s m a l l e r v a l u e of 400 ym as measured i n the model c o u l d be a t t r i b u t e d t o t h e s m a l l e r f i b e r den-s i t y w i t h which the MU was r e p r e s e n t e d . T h i e l e & Boehle used the DISA 13K53 e l e c t r o d e which had a c a n n u l a d i a m e t e r o f o n l y 450 um as compared t o t h e CNE under i n v e s t i g a t i o n w i t h 650 ym. T h i s c o u l d a l s o have an i n f l u e n c e on t h e p i c k u p a r e a . N e v e r t h e l e s s , t h e o b s e r v e d p i c k u p r a d i u s l a y w i t h i n 40% t o 60% o f t h e v a l u e s r e p o r t e d by S t a l b e r g and T h i e l e & B o e h l e . Peak-to-Peak D u r a t i o n The PTPD's r e c o r d e d w i t h t h e CN e l e c t r o d e d i d not e x h i b i t noteworthy d i f -f e r e n c s from the ones a l r e a d y p r e s e n t e d i n s e c t i o n 3.6 i n the case of t h e SFP. The f a c t was e a s i l y u n d e r s t a n d a b l e s i n c e the r e c o r d i n g d i s t a n c e of the c l o s e s t f i b e r , which e s s e n t i a l l y determines the PTPD, was never l a r g e r than r = 20 mm / 389 ym. The PTPD of the c a n n u l a s i g n a l was a t l e a s t double t h e PTPD of the c o r e s i g n a l w i t h i n r < 20 mm; c f . s e c t i o n 3.6 and F i g s . 3.8 and 3.9. F o r t h a t r e a s o n the PTPD o f the MUP d i f f e r e n t i a l s i g n a l 'core v s . c a n n u l a ' remained the same as f o r the SFP of the n e a r e s t f i b e r i n t h e a r r a y even though the c a n n u l a 84 500 -i 400 A 300 A CL 200 A 100 A MUP v SFP / point electrode } 'core vs remote" • MUP o SFP * MUP 1 a SFP J cannula vs remote • MUP \ . o SFP J core vs cannula' ' I 1 — " — 1 — r — | — i — r — • — i — | — i — i — i — i — | — i — i — i — i — j — i — r — t — i — ( — i — r 50 100 150 200 250 300 RECORDING D ISTANCE R (MICROMETERS) 350 400 F i g u r e 3 . 1 7 . The PTPA vs r o f the p o i n t e l e c t r o d e and c o m p l e t e CNE ( ' c o r e v s r e m o t e ' , ' c a n n u l a v s r e m o t e ' , ' c o r e vs c a n n u l a ' ) ; f r o n t SFP (y=0) and MUP. 85 p o t e n t i a l was over 60% of t h e c o r e PTPA ( F i g . 3.23). The f a c t o f unchanged PTPD's f o r s m a l l r e c o r d i n g d i s t a n c e s i n both SFP and MUP cases was not c o n t r a -d i c t o r y w i t h r e p o r t s found i n the l i t e r a t u r e . E k s t e d t (1964) measured a mean PTPD o f 112 ys f o r SFP's whereas B u c h t h a l (1955) o b t a i n e d a mean PTPD o f 121 ys f o r MUP's. The d i p o l e l e n g t h f o r t h i s i n v e s t i g a t i o n was chosen 2s = 500 ym i n o r d e r t o produce a s h o r t e s t PTPD o f 125 ys ( r = 25 ym) a t an assumed p r o p a g a -t i o n v e l o c i t y o f 4 m/s. Spike D u r a t i o n The main impact o f the l a r g e c a n n u l a MUP s i g n a l w i t h a l o n g PTPD was on t h e SD of t h e r e c o r d e d MUP. F i g u r e 3.18 i l l u s t r a t e s t h e m a s s i v e l y s h o r t e r SD o f the 'core v s . c a n n u l a ' MUP compared t o the 'core v s . remote' o r a l s o t r u e SD. While a t r = 50 ym t h e SD o f t h e d i f f e r e n t i a l s i g n a l was o n l y 50 ys s h o r t -e r t h a n the c o r e s i g n a l , t h e d i f f e r e n c e expanded t o 350 ys a t r = 300 ym. A l t h o u g h no SD e v a l u a t i o n s f o r r > 20 mm / 389 ym were made, the graphs i n d i -c a t e d a r a p i d l y i n c r e a s i n g d e f i c i t i n SD o f t h e 'core v s . c a n n u l a ' s i g n a l , compared t o the t r u e v a l u e . Another a s p e c t i n F i g . 3.18 i s o f i n t e r e s t . The SD's o f both 'core v s . remote* and 'core v s . c a n n u l a ' MUP s i g n a l s were l o n g e r f o r r < 180 ym and r < 120 ym, r e s p e c t i v e l y , t h a n t h e t r u e SD r e c o r d e d w i t h the p o i n t e l e c t r o d e . The same was o b s e r v e d f o r t h e SFP SD as a l r e a d y p r e s e n t e d i n s e c t i o n 3.6, F i g . 3.10, f o r r < 170 ym. The l o n g e r than t r u e SD c o u l d be e x p l a i n e d by t h e s m a l l e r t h a n t r u e PTPA f o r s m a l l r . The SD o f t h e c a n n u l a MUP s i g n a l was not i n c l u d e d i n F i g . 3.18 because i t was so l o n g ( o v e r 2 ms). T h i s l o n g SD r e s u l t e d from the v e r y f l a t PTPA v s . r c u r v e which was p r e s e n t e d i n F i g . 3.17. 1 0 0 0 - , RECORDING D I S T A N C E R (MICROMETERS) F i g u r e 3 . 1 8 . The SD v s r o f the p o i n t e l e c t r o d e and c o m p l e t e CNE ( ' c o r e v s r e m o t e ' , ' c o r e v s c a n n u l a ' ) ; f r o n t SFP (y=0) and MUP. CO a* 87 3.10 S p e c i a l E l e c t r o d e D e s i g n The r e s u l t s p r e s e n t e d so f a r demonstrated c l e a r l y t h a t t h e CNE i n t r o d u c e s a c o n s i d e r a b l e d i s t o r t i o n o f the s i g n a l s p i c k e d up from e i t h e r the SF o r MU s o u r c e . The main d i s t o r t i o n s were a f l a t t e r PTPA v s . r and SD v s . r b e h a v i o u r . The c h i e f " o f f e n d e r s " were the l a r g e e l l i p t i c a l l e a d i n g - o f f s u r f a c e as w e l l as t h e s i g n a l s p i c k e d up by the c a n n u l a . The q u e s t i o n a r o s e as t o whether o r n o t i t was p o s s i b l e t o improve the r e c o r d i n g f i d e l i t y o f the CNE by s i m p l e means. One p o s s i b i l i t y was t o reduce the l e a d i n g - o f f s u r f a c e . Such e l e c t r o d e s a r e g e n e r a l l y known as SF e l e c t r o d e s , where the c i r c u l a r , 25 um d i a m e t e r l e a d i n g -o f f s u r f a c e i s u s u a l l y embedded i n epoxy r e s i n i n a s i d e p o r t c l o s e t o t h e d i s -t a l end o f the n e e d l e . E x t e n s i v e l i t e r a t u r e about SFEMG e x i s t s . The o t h e r approach was t o t r y t o reduce t h e " h a r m f u l " c a n n u l a p o t e n t i a l s . F o r t h a t p u r -pose, the d i s t a l end o f the c a n n u l a was i n s u l a t e d 2 o v e r a l e n g t h of 215 mm / 4184 um. T h i s l e n g t h was d e t e r m i n e d by two f a c t o r s : ( i ) In o r d e r t o be s h i e l d e d from the u n d e s i r a b l e p o t e n t i a l s , most o f the c a n n u l a p o r t i o n w i t h i n the MU t e r r i t o r y had t o be i n s u l a t e d . The MU t e r r i t o r y i n the human b i c e p s b r a c h i i muscle was r e p o r t e d t o have an average diameter o f 5 mm, see s e c t i o n 3.8. ( i i ) The r e m a i n i n g bare p a r t of t h e c a n n u l a must s t i l l be s u f f i c i e n t l y exposed t o the muscle t i s s u e t o a c t as a good r e f e r e n c e (low p o t e n -t i a l , low impedance, e x t e r n a l n o i s e r e j e c t i o n ) . 'KRYLON' Enamel Spray P a i n t , Borden P r o d u c t s L t d . , Canada. 88 F i g u r e 3.20. The type I I improved CNE ( i n s u l a t e d c a n n u l a t i p w i t h b a r e a n n u l a r , e l l i p t i c p o r t i o n ) . 89 The i n s u l a t e d c a n n u l a e l e c t r o d e , 'type I * , i s p i c t u r e d i n F i g . 3.19. The c o n s t r u c t i o n o f such an e l e c t r o d e c o u l d be p r o b l e m a t i c i n r e a l i t y because t h e i n s u l a t i o n around t h e sharp t i p might wear o f f e a s i l y . A second, somewhat s i m p l e r d e s i g n , 'type I I ' , was t h e r e f o r e r e a l i z e d . I t i s shown i n F i g . 3.20. The c a n n u l a was i n s u l a t e d o v e r t h e same l e n g t h o f 215 mm b u t w i t h t h e e x c e p t i o n o f t h e a n n u l a r , e l l i p t i c p a r t o f the s t . s t . c a n n u l a t h a t i s f l u s h w i t h t h e b e v e l . That d e s i g n would a l l o w i n p r a c t i c e t h e g r i n d i n g o f t h e e l e c t r o d e b e v e l as recommended t o p r e v e n t a d u l l p o i n t , w i t h o u t a l t e r i n g t h e e f f e c t o f t h e i n s u l a t i o n . V e r y i n t e r e s t i n g and p r o m i s i n g r e s u l t s were o b t a i n e d w i t h t h e new d e s i g n s , e s p e c i a l l y w i t h t y p e I I , as d i s c u s s e d i n t h e ne x t p a r a g r a p h s . Cannula P o t e n t i a l F i g u r e 3.21 compares the c a n n u l a p o t e n t i a l (SFP) i n % o f t h e c o r e p o t e n -t i a l v s . z f o r t h e r e g u l a r , t y p e I and I I CNE. The c o m p l e t e l y i n s u l a t e d c a n -n u l a t i p (type I) CNE had a n e g l i g i b l y s m a l l c a n n u l a p o t e n t i a l f o r z < 150 y s . T h i s was e x p e c t e d , a c c o r d i n g t o d e s i g n f a c t o r ( i ) . The d i f f e r e n t i a l s i g n a l was t h e r e f o r e i d e n t i c a l w i t h t h e 'core v s . remote' s i g n a l which means t h a t t h e c a n n u l a was an i d e a l r e f e r e n c e e l e c t r o d e . L a t e r p o r t i o n s o f t h e SFP were p i c k e d up by t h e c a n n u l a w i t h a r a t i o o f up t o 10% a t z = 625 y s . I t was c o n -c l u d e d t h a t t h e SFP d i s t o r t i o n s (see F i g . 3.22 t o 3.28) p i c k e d up w i t h a t y p e I CNE were not due t o the c a n n u l a p o t e n t i a l b u t r a t h e r due t o f i e l d d i s t o r t i o n s from the l a r g e l e a d i n g - o f f s u r f a c e and the c a n n u l a ( d i r e c t i o n a l p r o p e r t i e s ) . The p a r t i a l l y i n s u l a t e d (type I I ) CNE p i c k e d up on i t s c a n n u l a a maximum o f 24% o f t h e c o r e p o t e n t i a l f o r r = 2.5 mm/ 48.7 ym and z = 140 ys. F o r r = 10 mm / 195 ym t h e r a t i o was reduced t o 8% a t t h e same v a l u e o f z. F o r z > 250 ys t h e p e r c e n t a g e o f t h e c a n n u l a p o t e n t i a l was i d e n t i c a l f o r a l l r = 2.5 t o 10 mm and r e a c h e d a v a l u e o f 24% a t z = 650 y s . The " p e a k i n g " c a n n u l a p o t e n t i a l c u r v e 90 100 -i 9Q - 'core vs remote" PTPA = 100% • type I, a l l r • type I I , r = 48.7 „m • type I I , r = 97.3 nm * type I I , r = 195 „m 80 - o regular CNE, average f o r a l l r < 400 „m 70 A 0 / 100 200 300 400 5 0 0 600 700 Z A X I S (MICROSECONDS! F i g u r e 3 . 2 1 . The c a n n u l a p o t e n t i a l 1n % o f the c o r e p o t e n t i a l vs z o f the r e g u l a r , t y p e I and t y p e II CNE. f o r v a r i o u s r; f r o n t SFP (y=0 ) . 91 around z = 140 us ( t h i s i s not a t t h e peak of the c o r e ! ) was due t o t h e bare a n n u l a r , e l l i p t i c c a n n u l a p o r t i o n which p i c k e d up an even h i g h e r p o t e n t i a l t h a n t h e r e g u l a r bare c a n n u l a ( d o t t e d graph, average o f a l l r ; f o r t h e e x a c t c u r v e s see F i g . 3.16, s e c t i o n 3.9). F i g u r e 3.22 shows the same graphs as t h e p r e c e d i n g f i g u r e but f o r t h e MUP's. Not i n c l u d e d were the r e s u l t s o f t h e ty p e I I new d e s i g n (they were not computed; see a l s o remarks i n t h e pa r a g r a p h s 'PTPA' and 'SD' i n t h i s s e c t i o n ) . A t z = 50 us a f t e r the b a s e l i n e i n t e r s e c t i o n , t h e p e r c e n t a g e o f t h e ty p e I c a n n u l a p o t e n t i a l ranged from 3.5% t o 21.5% o f t h e c o r e p o t e n t i a l ( r = 2.5 t o 20 mm / 48.7 t o 389 um) w h i l e a t z = 600 us t h e p e r c e n t a g e s were between 52% and 56%. F i g u r e 3.23 p r e s e n t s a somewhat d i f f e r e n t a s p e c t o f t h e c a n n u l a p o t e n t i a l . P l o t t e d were t h e graphs o f t h e c a n n u l a p o t e n t i a l i n % o f t h e c o r e PTPA v s . r ( c o r r e s p o n d i n g t o the "peak of t h e c o r e " l i n e s i n F i g . 3.21 and 3.22). The t y p e I MU c a n n u l a p o t e n t i a l was re d u c e d w . r . t . t h e r e g u l a r bare c a n n u l a from 10% t o 3.5% a t r = 2.5 mm / 48.7 um and from 66% t o 24% a t r = 20 mm / 389 um. F o r comparison, the c o r r e s p o n d i n g graphs o f t h e r e g u l a r , t y p e I and I I c a n n u l a a r e a l s o g i v e n f o r the SFP. A l l t h r e e t y p e s had c a n n u l a p o t e n t i a l s s m a l l e r t h a n 5% o f t h e c o r e PTPA where r < 20 mm / 389 um. The ty p e I c a n n u l a p o t e n -t i a l was even s l i g h t l y n e g a t i v e ( i n v e r s e d p h a s e s ) . Peak-to-peak Amplitude The type I had a l a r g e r " i n s u l a t i n g w a l l " s u r r o u n d i n g the c o r e than t h e r e g u l a r CNE, due t o the i n s u l a t e d , a n n u l a r c a n n u l a p o r t i o n i n t h e b e v e l s u r -f a c e . T h e r e f o r e t h e SF PTPA 'core v s . remote' was s l i g h t l y l a r g e r ( c u r v e not shown) but o n l y f o r r > 2.5 mm / 48.7 um. The ty p e I I b e v e l was i d e n t i c a l w i t h 92 F i g u r e 3 . 2 2 . The c a n n u l a p o t e n t i a l i n % o f the c o r e p o t e n t i a l vs z o f the r e g u l a r and t y p e I CNE: MUP. / 60 A 50 A • MUP, type I • MUP, r e g u l a r v SFP, type I o SFP, r e g u l a r • SFP, type II 40 A 30 A 20 A 100 200 300 RECORDING D I S T A N C E R (MICROMETERS) 400 F i g u r e 3 . 2 3 , The c a n n u l a p o t e n t i a l In % of the c o r e PTPA vs r o f t h e r e g u l a r , t ype I and t y p e II CNE: f r o n t SFP (y=0) and MUP. 94 t h e r e g u l a r b e v e l . As e x p e c t e d , the PTPA 'core v s . remote' r e c o r d e d w i t h t y p e I I was i d e n t i c a l as w i t h the r e g u l a r CNE (no e x p l i c i t r e s u l t s shown). F i g u r e 3.24 compares t h e SF PTPA 'core v s . c a n n u l a ' o f t h e r e g u l a r , t y p e I and I I CNE. No r e a l improvement was a c h i e v e d w i t h e i t h e r t y p e I o r I I . Type I r e c o r d e d a s l i g h t l y l a r g e r PTPA than the r e g u l a r CNE f o r r > 2.5 mm /48.7 ym, due t o t h e more pronounced w a l l e f f e c t . A l t h o u g h t h e c a n n u l a p o t e n t i a l o f type I / I I was g r e a t l y d e c r e a s e d f o r l a r g e v a l u e s o f z ( F i g . 3.21) compared t o t h e r e g u l a r CNE, t h e p e r c e n t a g e o f the c a n n u l a p o t e n t i a l a t t h e peak o f t h e c o r e ( d o t t e d "peak" l i n e i n F i g . 3.21) was s m a l l e r t h a n 1% f o r a l l t h r e e t y p e s . T h e r e f o r e the PTPA 'core v s . c a n n u l a * remained t h e same w i t h t y p e I I and i n c r e a s e d o n l y s l i g h t l y w i t h type I , as compared t o the r e g u l a r CNE. Type I seemed t o r e c o r d a 2% t o 3% s m a l l e r PTPA than t h e r e g u l a r CNE f o r r < 2.5 mm / 48.7 ym. No measurements were made below r = 2.5 mm; t h e c u r v e was e x t r a p o -l a t e d ( d o t t e d i n F i g . 3.24). Measurement e r r o r s c o u l d n o t be r u l e d o u t s i n c e f o r s m a l l r t h e r e was a v e r y h i g h f i e l d g r a d i e n t . In F i g . 3.25 the r e s u l t s f o r t h e MUP a r e shown. Now th e g r e a t l y r e d u c e d c a n n u l a p o t e n t i a l (see F i g . 3.22) r e s u l t e d i n an enhanced 'core v s . c a n n u l a ' PTPA o f type I f o r l a r g e r , compared t o the r e g u l a r CNE. The p i c k u p r a d i u s was t h e r e f o r e r a i s e d t o about 520 ym w i t h t y p e I as opposed t o t h e 400 ym measured w i t h th e r e g u l a r CNE (see remark i n s e c t i o n 3 .9). I f t h e improvement f a c t o r 520/400 = 1.3 were a p p l i e d t o t h e r e p o r t e d p i c k u p r a d i i o f 700 t o 1000 ym ( r e f . i n s e c t i o n 3.9) , an improved p i c k u p r a d i u s w i t h t h e type I CNE o f 910 t o 1300 ym i n r e a l i t y would r e s u l t . Under the assumption of a CNE l o c a t i o n a t about t h e c e n t e r o f an average MU, t h e f a r t h e s t MU f i b e r s would be a t r = 2.5 mm. The p i c k u p r a d i u s o f up t o 1.3 mm would c o n s t i t u t e a n i c e l y improved f i d e l i t y o f r e c o r d i n g . The MU PTPA f o r t y p e I I was n o t e v a l u a t e d because o n l y t h e measurements f o r the SFP a t y = 0 were r e c o r d e d ( F i g . 3.24). T e s t measurements 95 I ' ' ' ' I ' ' 1 ' I 1 1 • 1 I ' ' • • I • i i i ) i i i i I i i i i ! i i i i ! 0 50 100 150 200 250 300 350 400 RECORDING D ISTANCE R (MICROMETERS) F i g u r e 3 . 2 4 . The PTPA v s r o f the p o i n t e l e c t r o d e , r e g u l a r , t y p e I and t y p e II CNE ( ' c o r e v s c a n n u l a ' ) ; f r o n t SFP (y=o). 0 •( i i i i I i — r — i — i — i — i — i — i — i — | — i — i — i — i — | — i i i — i — | i i — i — i — r - i — i — i — i — | — i — i — i — i — | 0 50 100 150 200 250 300 350 400 RECORDING DISTANCE R (MICROMETERS) F i g u r e 3 . 2 5 . The PTPA vs r o f the p o i n t e l e c t r o d e , r e g u l a r , t y p e I and t y p e II CNE ( ' c o r e v s r e m o t e ' , ' c a n n u l a v s r e m o t e ' , ' c o r e vs c a n n u l a ' ) ; MUP. 97 from front and back SFP's at various levels of y (other than y = 0) indicated that the type II recorded very similar 'core vs. remote' and 'cannula vs. remote' signals as the type I CNE (no results shown). Since the 'core vs. cannula' PTPA of type I and II (in Fig. 3.24) differed less than 10% for r < 100 um, where the influence on the MUP is most pronounced, i t was concluded that the MU PTPA 'core vs. cannula' of type II must be essentially the same as type I. Finally, Fig. 3.26 shows the deviation in % from the true MU PTPA (point electrode) when measured differentially 'core vs. cannula* with the regular and the type I/type II (see remark above) CN electrode. The higher f i d e l i t y of the new designs I, II is clearly v i s i b l e , especially for r > 300 ym where the "steepness" of deviation was less pronounced. Peak-to-peak Duration No changes were anticipated with the new design. Therefore no measure-ments were made. Spike Duration Figure 3.27 shows the comparison of the graphs for the SFP SD recorded with the point, regular, type I and type II CNE. The larger SD recorded with type I (compared to the regular CNE) resulted in a smaller deviation from the true value than the regular CNE for r > 200 ym, while for r < 200 ym the type I was worse than the regular CNE. The type I recorded a longer SD for a l l r than the regular CNE, due to the greatly reduced cannula potential (Fig. 3.21) for z > 100 ys, compared to the regular CNE. The SD is dependent on the shape of the AP after the peak. Hence the cannula potential at large values of z is deter-mining the SD. 140 - i RECORDING DISTANCE R (MICROMETERS) F i g u r e 3 . 2 6 . The PTPA i n % of the t r u e PTPA vs r o f the r e g u l a r , t y p e I and t y p e II CNE ( ' c o r e vs c a n n u l a ' ) ; MUP. U3 00 F i g u r e 3 . 2 7 , The SD v s r o f the p o i n t e l e c t r o d e , r e g u l a r , t y p e I and t y p e II CNE ( ' c o r e vs c a n n u l a ' ) ; f r o n t SFP vo (y=o). vo 100 The PTPA, however, i s d e t e r m i n e d by t h e c a n n u l a p o t e n t i a l o n l y a t t h e peak o f t h e c o r e p o t e n t i a l (which was almost t h e same r a t i o o f l e s s t h a n 1% f o r a l l e l e c t r o d e t y p e s ; t h e r e f o r e t h e PTPA d i d n o t undergo d r a s t i c c h a n g e s ) . The t y p e I I d e s i g n r e c o r d e d the SD w i t h t h e h i g h e s t f i d e l i t y . F o r r > 350 ym i t s SD was o n l y 20 ys s h o r t e r than type I but f o r r < 150 ym t h e SD was even s h o r t e r than w i t h t h e r e g u l a r CN e l e c t r o d e . W i t h i n r = 50 ym t o 400 ym t h e d e v i a t i o n from t h e t r u e v a l u e was never more than ±35 y s . T h i s improvement can be e x p l a i n e d a g a i n w i t h F i g . 3.21. F o r v a l u e s of z > 200 y s , t h e t y p e I and I I c a n n u l a p o t e n t i a l s d i f f e r e d o n l y 10% t o 15%. Those l a t e AP p o r t i o n s d e t e r m i n e d t h e SD f o r t h e v a l u e s o f r > 250 ym i n F i g . 3.27, where i n d e e d o n l y a s m a l l d i f -f e r e n c e o f 20 ys between type I and I I o c c u r r e d . A t z » 140 ys, however, t y p e I I had a c a n n u l a p o t e n t i a l o f max. 24% o f t h e c o r e p o t e n t i a l a t r — 2.5 mm / 48.7 ym ( F i g . 3.21) which was more than th e r e g u l a r bare c a n n u l a (about 3% a t r = 48.7 ym; see F i g . 3.16). Type I had a p p r o x i m a t e l y z e r o v o l t a g e on t h e c a n n u l a . So t h e l a r g e c a n n u l a p o t e n t i a l o f t y p e I I around z = 140 ys l o w e r e d t h e SD even below the v a l u e o f t h e r e g u l a r CNE SD f o r r < 150 ym. In F i g . 3.28 t h e SD c u r v e s a r e p l o t t e d f o r t h e MUP c a s e . The d i f f e r e n c e s were s t i l l more pronounced. The e x t r e m e l y s h o r t SD r e c o r d e d w i t h t h e r e g u l a r CNE a t r = 300 ym (500 ys s h o r t e r t ha n t r u e v a l u e ) was b r o u g h t up w i t h t y p e I t o a d i f f e r e n c e o f o n l y -130 ys from the t r u e v a l u e . However, a t r = 50 ym, t y p e I r e c o r d e d a 80 ys l o n g e r SD th an the t r u e v a l u e w h i l e t h e r e g u l a r CN o n l y y i e l d e d a 30 ys l o n g e r SD. T h i s was due t o t h e g r e a t l y r e d u c e d type I c a n n u l a MUP compared t o the r e g u l a r CNE ( F i g . 3.22). F i g u r e 3.28 a l s o c o n t a i n s an e s t i m a t e d SD c u r v e of t h e t y p e I I CNE (no complete MU measurements were c a r r i e d o u t w i t h type I I ) . The v a l i d i t y o f t h e e s t i m a t e was s u p p o r t e d by t h e f o l l o w i n g f a c t o r s : SD. (MICROSECONDS) IV) o o o o o cn o o CO o o o o CO o o 03 O o o o o IS 0 B) H C 3 3-T a n> < <B (/I rt- O 0 < -* T> < ro ui rt-(D >—* •i o rt- rt> < •a O r+ IB Z -J m (D -« 13 0 o - — Z 0 D m o <+ i — to <B UI — ID o < n (BOO ui a rt- 3 m 3 • 3 C 0) — 1 rt- 0) (D CD -(Q - w C IB T (B 2 -c rt- "0 rt-(B • < X 73 rt- -) (D • J (B « \ v\ 4 <• O • 0 < < o • *><=> n i o a 3D a cn a CO m 3D o — i CO m o • 33 o CO o 101 102 - The MU PTPA 'core v s . c a n n u l a ' was t h e same f o r the r e g u l a r and t y p e I I CNE ( F i g . 3.25). - The f a r f i b e r s have the same e f f e c t on t h e t y p e I o r I I c a n n u l a p o t e n t i a l ( t h i s was mentioned i n c o n t e x t w i t h the d e s c r i p t i o n o f F i g . 3.25). - For s m a l l r , t h e type I I c a n n u l a SFP was much l a r g e r than t y p e I around z = 140 ys ( F i g . 3.21). - F o r s m a l l r , i t can be e x p e c t e d t h a t a l s o t h e c a n n u l a MUP o f t y p e I I ( i n % of t h e c o r e p o t e n t i a l ) i s " p e a k i n g " around z « 100 t o 200 ys because t h e MUP i s t h e sum of t h e SFP's. - I t can be assumed t h a t f o r r < 5 t o 10 mm / 97.3 t o 195 ym t h e " p e a k i n g " t y p e I I c a n n u l a MUP reaches a t l e a s t the c o r r e s p o n d i n g v a l u e s of the r e g u l a r c a n n u l a MUP (comparison o f t h e SFP case i n F i g . 3.16 and 3.21, where f o r r = 2.5 mm / 48.7 ym t h e t y p e I I c a n n u l a p o t e n t i a l was 36% l a r g e r t h a n the r e g u l a r c a n n u l a p o t e n t i a l , and f o r r > 10 t o 15 mm / 195 t o 292 ym both p o t e n t i a l s were a p p r o x i m a t e l y t h e same). F o r l a r g e r r and z, both t y p e I and t y p e I I c a n n u l a MUP's would be v e r y s i m i l a r . Those f a c t o r s j u s t i f y the e s t i m a t e d c u r v e of t h e SD f o r t h e t y p e I I CNE i n F i g . 3.28. I t i s a worst case r e p r e s e n t a t i o n where t h e improvement i n the SF case ( F i g . 3.27) was a t t r i b u t e d t h e same or s l i g h t l y s m a l l e r r e l a t i v e v a l u e i n t h e MU c a s e . T h e r e f o r e a t r = 50 ym, t h e e s t i m a t e d t y p e I I SD was s e t e q u a l t o t h e r e g u l a r CNE SD w h i l e f o r r > 300 ym t h e e s t i m a t e c o i n c i d e d w i t h t y p e I . F i n a l l y , F i g . 3.29 i l l u s t r a t e s t h e d e v i a t i o n i n % from t h e t r u e SD f o r t h e r e g u l a r , type I and type I I CN e l e c t r o d e . The graph of the l a t t e r c o r r e s p o n d e d t o t h e e s t i m a t e as i n F i g . 3.28. F o r r = 50 t o 350 ym, t h e e s t i m a t e d SD never d i f f e r e d by more than ±20% from the t r u e v a l u e - a r a t h e r c o n s i d e r a b l e improve-ment i n the r e c o r d i n g f i d e l i t y . o CO 140 -i 130 A 120 A n o A 100 point electrode - true SD v regular o type I (• 'core vs cannula' • type II (ESTIMATE) 100 200 300 RECORDING DISTANCE R (MICROMETERS) 400 F i g u r e 3 . 2 9 . The SD In % o f the t r u e SD v s r o f the r e g u l a r , t y p e I and t y p e II CNE ( ' c o r e vs c a n n u l a ' ) ; MUP. The c u r v e o f the t y p e II CNE 1s an e s t i m a t e , see t e x t . U) 1 0 4 L e a r n i n g w i t h o u t thought i s l a b o u r l o s t ; Thought w i t h o u t l e a r n i n g i s p e r i l o u s . C o n f u c i u s ( A n a l e c t s ) IV. CONCLUSIONS AND RECOMMENDATIONS 105 4.1 C o n c l u s i o n s In t h i s i n v e s t i g a t i o n an e l e c t r o l y t i c tank model o f an a c t i v e muscle f i b r e has been devel o p e d f o r the measurement of the r e c o r d i n g and d i s t o r t i n g p r o p e r -t i e s o f the c o n c e n t r i c n e e d l e e l e c t r o d e . E l e c t r o l y t i c tank models f o r s p e c i f i c measurements were mentioned ("wall e f f e c t " ; E k s t e d t , 1964 u n p u b l i s h e d ) o r r e -p o r t e d ( f o r example " e l e c t r o d e impedance"; P o l l a k , 1974 a,b,c) but no r e p o r t about a complete e x p e r i m e n t a l tank model i n v e s t i g a t i o n w i t h CN o r SF e l e c t r o d e s was f o u nd i n t h e l i t e r a t u r e . The model was b a s e d on t h e d i p o l e c o n c e p t i n an e x t e n s i v e volume c o n d u c t o r . Frequency e f f e c t s from the near f i e l d c o u l d not be modeled. In a d d i t i o n , a x i a l d i p o l e d i s p e r s i o n was not t a ken i n t o a c c o u n t i n t h e motor u n i t c a l c u l a t i o n s . F i e l d D i s t o r t i o n s T h r e e b a s i c d i s t o r t i n g e f f e c t s t a k i n g p l a c e a t t h e e l l i p t i c (150 um x 580 ym r e a l dimensions) l e a d i n g - o f f s u r f a c e were i n v e s t i g a t e d : • S h u n t i n g of volume c o n d u c t o r c u r r e n t s by the m e t a l - t i s s u e i n t e r f a c e im-pedances. The s p e c i f i c i n t e r f a c e impedances were v e r y l a r g e f o r p l a t i n u m , g o l d o r s t a i n l e s s s t e e l compared t o the b u l k r e s i s t i v i t y of t h e e l e c t r o -l y t e . T h e r e f o r e o n l y a l i t t l e s h u n t i n g was e x p e c t e d . The PTPA d e c r e a s e due t o s h u n t i n g was maximum 22% from the t r u e PTPA f o r a r e c o r d i n g d i s -t a n c e of r = 50 ym and l e s s than 10% f o r r = 200 ym. S h u n t i n g was the weakest o f a l l d i s t o r t i n g e f f e c t s . E k s t e d t (1964) and S t a l b e r g and T r o n t e l j (1979) mentioned the s h u n t i n g as a p o s s i b l e o r even major d i s -t o r t i n g f a c t o r ( f r e q u e n c y dependent) but no q u a n t i t a t i v e r e s u l t s were r e p o r t e d . • The " m e t a l l i c w a l l e f f e c t " o r e l e c t r i c a l i m a g i n g o f the d i p o l e s o u r c e a t the l e a d i n g - o f f s u r f a c e . The l e s s s h u n t i n g t h e r e i s , t h e more the 106 m e t a l l i c s u r f a c e appears as an i n s u l a t o r i n t h e e l e c t r o l y t e . The PTPA i n c r e a s e due t o t h e w a l l e f f e c t of a pure i n s u l a t o r o f t h e s i z e and e l l i p -t i c shape of the c o r e was o v e r 99% f o r r e c o r d i n g d i s t a n c e s r < 50 ym ( " f u l l " w a l l e f f e c t ; d o u b l i n g of the p o t e n t i a l ) . F o r l a r g e r r e c o r d i n g d i s t a n c e s t h e PTPA i n c r e a s e was d i m i n i s h e d r a p i d l y due t o t h e f i n i t e s i z e o f t h e i n s u l a t o r . L e s s t h a n 10% i n c r e a s e was r e c o r d e d f o r r > 780 ym. The " l e s s - t h a n - p e r f e c t i n s u l a t o r P t " c a u s e d a d i m i n i s h e d w a l l e f f e c t o f 56% PTPA i n c r e a s e a t r = 50 ym (or a 22% d e c r e a s e d f u l l w a l l e f f e c t due t o s h u n t i n g ; see p r e c e d i n g p a r a g r a p h ) . I t s h o u l d be n o t e d t h a t t h e r e s u l t s were f o r the PTPA o n l y . Other p o r t i o n s of t h e AP a f t e r t h e peak were much l e s s enhanced than around the peak. T h e r e f o r e a shape d i s t o r t i o n was i n t r o d u c e d by the w a l l e f f e c t ( s h o r t e n e d SD). E k s t e d t (1964) a l s o men-t i o n e d t h e " m e t a l l i c w a l l e f f e c t " ( f r e q u e n c y dependent) b u t r e p o r t e d no q u a n t i t a t i v e r e s u l t s . • The p o t e n t i a l a v e r a g i n g a l o n g t h e m e t a l l i c l e a d i n g - o f f s u r f a c e d e c r e a s e s the measured p o t e n t i a l compared t o t h e p o t e n t i a l a t t h e c e n t e r of t h e s u r f a c e . A v e r a g i n g i s most pronounced i n t h e near f i e l d w i t h a h i g h f i e l d g r a d i e n t and i n e f f e c t i v e i n the f a r f i e l d where the g r a d i e n t approaches z e r o . The PTPA d e c r e a s e due t o "pure a v e r a g i n g " was 67% from t h e t r u e PTPA a t a r e c o r d i n g d i s t a n c e of 50 ym. L e s s t h a n 10% was r e c o r d e d a t d i s t a n c e s o f more than 720 ym. The e f f e c t s o f a v e r a g i n g were computer s i m u l a t e d by E k s t e d t and S t a l b e r g (1973). No d i r e c t comparison of the s i m u l a t e d and measured r e s u l t s was p o s s i b l e because t h e d i p o l e l e n g t h s were d i f f e r e n t . The i n d i v i d u a l and compound c o n t r i b u t i o n s t o t h e AP d i s t o r t i o n s of t h o s e t h r e e " c o r e " f a c t o r s have not been p r e v i o u s l y q u a n t i f i e d . 107 The i n s u l a t i o n s u r r o u n d i n g t h e c o r e i n t r o d u c e d an a d d i t i o n a l , " r e g u l a r " w a l l e f f e c t , r e s u l t i n g i n a PTPA i n c r e a s e f o r a l l r e c o r d i n g d i s t a n c e s r . T h i s "enhanced w a l l e f f e c t " ( " m e t a l l i c " and " r e g u l a r " w a l l e f f e c t ) f u r t h e r deempha-s i z e d t h e r e l a t i v e c o n t r i b u t i o n o f s h u n t i n g . I n t h e near f i e l d , t h e PTPA i n -c r e a s e was 40% t o 45% of the v a l u e r e c o r d e d w i t h t h e 'core* a l o n e ( i n c o r p o r a t -i n g s h u n t i n g , w a l l e f f e c t and a v e r a g i n g ) , w h i l e i n t h e f a r f i e l d t h e i n c r e a s e was i n t h e o r d e r of 25% t o 35%. Other AP p o r t i o n s ( a f t e r t h e peak) were much l e s s enhanced than around t h e peak which r e s u l t e d i n a s h o r t e n e d SD. E k s t e d t (1964) s t a t e d t h a t the w a l l e f f e c t d i d not a l t e r t h e shape o f t h e r e c o r d e d AP. O v e r a l l D i s t o r t i o n s The complete CNE i n t h e d i f f e r e n t i a l r e c o r d i n g mode 'core v s . c a n n u l a ' p i c k e d up a SFP w i t h the f o l l o w i n g d i s t o r t i o n s . F o r v e r y s m a l l r + 25 im t h e PTPA was a t t e n u a t e d by 30% from t h e t r u e v a l u e and a t r = 500 ym t h e r e was an i n c r e a s e of about 10%. A t r = 1800 um t h e r e was an a t t e n u a t i o n a g a i n o f 30% w h i l e t h e 'co r e ' p o t e n t i a l a l o n e was d e c r e a s e d o n l y by 10% from t h e t r u e v a l u e ( l a r g e c a n n u l a s i g n a l ) . The c a n n u l a i n t r o d u c e d a v e r y s t r o n g d i r e c t i o n a l e f f e c t . A SFP a t the back o f the b e v e l (almost t o u c h i n g t h e cann u l a ) p r o d u c e d a c o r e p o t e n t i a l t h a t was o n l y 10% o f t h e t r u e v a l u e a t r = 325 ym and j u s t o v e r 40% a t r = 1600 ym. The c a n n u l a p o t e n t i a l was even l a r g e r than t h e c o r e p o t e n t i a l so t h a t t h e d i f f e r e n t i a l s i g n a l was n e g a t i v e ! See comment below c o n c e r n i n g t h e c a n n u l a p o t e n t i a l . A l s o t h e PTPD and SD d i f f e r e d from t h e t r u e v a l u e s i n t h e f a r f i e l d . The PTPD was o n l y 75% o f the t r u e v a l u e a t r = 1600 ym, and t h e SD o n l y 70% o f t h e t r u e v a l u e a t r = 800 ym. A s i m p l i f i e d MU was de v e l o p e d r e p r e s e n t i n g a s m a l l f i b e r d e n s i t y o f about 2-3 f i b e r s / m m 2 . A simple s p a t i a l arrangement o f the f i b e r s f a c i l i t a t e d the e v a l u a t i o n of the c o n t r i b u t i o n t o t h e PTPA, PTPD and SD from t h e near and 108 d i s t a n t f i b e r s . Both PTPA and SD were d i s t o r t e d i n t h e near and f a r f i e l d w h i l e the PTPD remained e s s e n t i a l l y t h e same as from a SFP, f o r a l l r . ' The PTPA was about 75% of the t r u e v a l u e a t r = 50 um, r e a c h e d a l m o s t 90% a t r = 250 um and a t r = 400 um t h e PTPA was o n l y 5% o f i t s v a l u e f o r r •*• 25 ym. Thus a " p i c k u p r a d i u s " o f 400 ym was d e t e r m i n e d which i s o n l y about h a l f o f the p i c k u p r a d i i r e p o r t e d i n t h e l i t e r a t u r e ( T h i e l e and B o e h l e , 1975; S t a l b e r g and T r o n t e l j , 1979). The s m a l l e r o b s e r v e d v a l u e was a t t r i b u t e d t o t h e r e l a t i v e l y s m a l l f i b e r d e n s i t y o f the MU model under i n v e s t i g a t i o n . The SD was about 40 ys l o n g e r than t h e t r u e v a l u e a t r = 50 ym but a l r e a d y a t r = 250 ym t h e CNE p i c k e d up a SD which was s h o r t e r by 55% o f the t r u e v a l u e - a r a t h e r c o n s i d e r -a b l e shape d i s t o r t i o n . Cannula P o t e n t i a l The c a n n u l a p o t e n t i a l was found t o undergo s m a l l changes f o r d i f f e r e n t i n s e r t i o n depths when c o n s i d e r i n g o n l y one f i b e r g e n e r a t o r a t a f i x e d r e l a t i o n -s h i p t o the p i c k u p s u r f a c e . The p o t e n t i a l d e c r e a s e was a p p r o x i m a t e l y p r o p o r -t i o n a l to. t h e i n c r e a s e i n i n s e r t i o n depth. However, the a b s o l u t e c a n n u l a p o t e n t i a l was g r e a t l y dependent on the r e l a t i v e p o s i t i o n o f t h e f i b e r s t o t h e core and the c a n n u l a . Cannula p o t e n t i a l s of w e l l o v e r 100% of t h e c o r e p o t e n -t i a l were found when a f i b r e was c l o s e t o t h e c a n n u l a but f a r from t h e c o r e . T h i s means t h a t i n the case of a MU, where o n l y a few f i b e r s a r e near t h e c o r e (which c o n t r i b u t e t o t h e most s i g n i f i c a n t p a r t of the MUP) but many f i b e r s near the l a r g e c a n n u l a , the c a n n u l a p o t e n t i a l can r e a c h l a r g e v a l u e s . Cannula p o t e n t i a l s o f 10% t o 65% of the c o r e PTPA were measured, where the r e c o r d i n g d i s t a n c e of the n e a r e s t f i b e r was between r = 50 ym t o 400 ym. A SF f a c i n g t h e c o r e produced f o r the same v a l u e s of r o n l y a c a n n u l a p o t e n t i a l o f 0.5% t o 4.5% o f the core PTPA. For l a t e r p o r t i o n s of the MUP ( a f t e r the p e a k ) , t h e c a n n u l a 109 p o t e n t i a l was up t o p r a c t i c a l l y 100% o f the c o r e p o t e n t i a l a t z = 750 us ( a l l r ) w h i l e i n t h e case of a f a c i n g SF t h e c o r r e s p o n d i n g v a l u e was about 60%. The e f f e c t s of those l a r g e MU c a n n u l a p o t e n t i a l s were t o d i s t o r t t h e PTPA and SD as d e s c r i b e d above. A q u a n t i t a t i v e assessment of the r e l a t i o n s between c a n n u l a i n s e r t i o n depth, MU f i b e r arrangement, c a n n u l a p o t e n t i a l shape and a m p l i t u d e and t h e r e s u l t i n g d i s t o r t i o n i n PTPA and SD of the d i f f e r e n t i a l s i g n a l 'core v s . c a n n u l a ' has not been p r e v i o u s l y done. S p e c i a l emphasis s h o u l d be l a i d on t h e f a c t t h a t t h e i n s e r t i o n depth of the c a n n u l a i s o f l e s s importance th an t h e p r o x i m i t y and number of nearby f i b e r s t o t h e c a n n u l a . T h i s was h i t h e r t o un-documented. E l e c t r o d e Improvements F i n a l l y , two new d e s i g n s of t h e CNE were t e s t e d which took t h e above know-ledge i n t o a c c o u n t . The d e s i g n t h a t seemed more e a s i l y r e a l i z a b l e a l s o ex-h i b i t e d a g r e a t e r improvement towards a h i g h e r r e c o r d i n g f i d e l i t y o f t h e CNE. An i n s u l a t e d d i s t a l end o f the c a n n u l a , e x c e p t f o r t h e a n n u l a r p a r t t h a t i s f l u s h w i t h t h e c o r e and i n s u l a t i o n , s h i e l d e d o f f a g r e a t d e a l of t h e " h a r m f u l " c a n n u l a p o t e n t i a l s . Both PTPA and SD came c l o s e r t o t h e t r u e v a l u e t h a n t h e r e g u l a r CNE, f o r e i t h e r a SFP o r MUP. The PTPD remained unchanged. The MU PTPA was l a r g e r t h a n w i t h t h e r e g u l a r CNE which r e s u l t e d i n e x t e n d i n g t h e " p i c k u p r a d i u s " by 30% t o 520 um. T h i s i s a v e r y i m p o r t a n t f e a t u r e because v a r i o u s neuromuscular d i s o r d e r s a r e not o b v i o u s i n any s e c t i o n of t h e MU. The r e l a t i v e l y s m a l l p i c k u p r a d i u s of the r e g u l a r CNE r e p r e s e n t s o n l y about 5% t o 10% o f the whole MU t e r r i t o r y ( S t a l b e r g and A n t o n i , 1980). The extended p i c k u p r a d i u s o f t h e improved CNE would t h e r e f o r e r e p r e s e n t a l a r g e r p o r t i o n o f t h e MU, p o s s i b l y up t o 25%. The MU SD of the improved CNE r e a c h e d almost 90% of t h e t r u e v a l u e a t r = 250 um, as opposed t o the 45% w i t h the r e g u l a r CNE. F o r 110 s m a l l e r r , a worst case e s t i m a t e of the SD approached the v a l u e r e c o r d e d w i t h t h e r e g u l a r CNE which was about 10% l a r g e r t h a n t h e t r u e v a l u e ( r = 50 um) . Summary Thus the major new f i n d i n g s i n t h i s i n v e s t i g a t i o n were: • The q u a n t i f i c a t i o n of the " s h u n t i n g of volume c o n d u c t o r c u r r e n t s " , " w a l l e f f e c t " ( f o r a c r y l i c g l a s s and Pt) and " p o t e n t i a l a v e r a g i n g " showed t h a t " s h u n t i n g " was t h e weakest f i e l d d i s t o r t i n g e f f e c t a t t h e m e t a l l i c l e a d i n g - o f f s u r f a c e . • The p r e s e n c e of the c a n n u l a d i s t u r b e d t h e f a r f i e l d a p p r e c i a b l y ( s m a l l e r PTPA, PTPD and SD). • The motor u n i t p o t e n t i a l was p i c k e d up by the c o n c e n t r i c n e e d l e e l e c t r o d e w i t h c o n s i d e r a b l y s m a l l e r a m p l i t u d e s i n t h e near f i e l d and s p i k e d u r a t i o n s i n t h e f a r f i e l d . • The i n s e r t i o n depth o f t h e c a n n u l a was o f much l e s s i n f l u e n c e on t h e c a n n u l a p o t e n t i a l than the p r o x i m i t y and number of nearby f i b e r s . • A s i m p l e way o f i m p r o v i n g the r e c o r d i n g f i d e l i t y o f the c o n c e n t r i c n e e d l e e l e c t r o d e was d e s i g n e d and e x p e r i m e n t a l l y t e s t e d . The main improvement was i n t h e SD of the near and f a r f i e l d (SFP and MUP) and i n t h e PTPA of t h e f a r f i e l d (SFP and MUP). 4.2 Recommendations The p r o m i s i n g t y p e I I new CNE d e s i g n c o u l d be more t h o r o u g h l y i n v e s t i -g a t e d . E s p e c i a l l y d i f f e r e n t i n s u l a t i o n l e n g t h s and m o d i f i c a t i o n s i n t h e bare a n n u l a r c a n n u l a p o r t i o n a t t h e t i p s h o u l d be t e s t e d . The l a t t e r i s i m p o r t a n t because i n p r a c t i c e t h e b a r e c a n n u l a p o r t i o n might n o t be as c l e a r - c u t as F i g . 3.20 shows. The r e g r i n d i n g o f the t i p and removal of the b u r r as w e l l as the 111 use of the n e e d l e a r e l i k e l y t o cause an a b r a s i o n of t h e i n s u l a t i o n a t t h e s h a f t around t h e b e v e l . C l i n i c a l t e s t i n g o f t h e new d e s i g n i s s t r o n g l y u r g e d . Comparisons of a l a r g e number o f r e s u l t s from a r e g u l a r CNE and t h e improved one would h o p e f u l l y c o n f i r m t h e r e s u l t s f o u nd i n t h e e l e c t r o l y t i c tank model. Other ways might be sought t o d e v e l o p a n o t h e r " o p t i m a l " e l e c t r o d e . A " d o u b l e -b e v e l " t i p , i f r e a l i z a b l e , i s an example t o r e d u c e t h e d i r e c t i o n a l p r o p e r t y o f the CNE. No i n v e s t i g a t i o n s were made w i t h o t h e r t y p e s o f CNE's t h a n t h e one d e s c r i b e d i n T a b l e 2.1. C o m m e r c i a l l y a v a i l a b l e CN e l e c t r o d e s come i n o u t e r d i a m e t e r s of 0.3 t o 0.9 mm and P t l e a d i n g - o f f a r e a s of 0.015 t o 0.07 mm (examples from DISA). I t can be e x p e c t e d t h a t t h e s m a l l e r c a n n u l a d i a m e t e r s and l e a d i n g - o f f s u r f a c e s cause d i f f e r e n t d i s t o r t i o n s t h a n measured i n t h i s i n v e s t i g a t i o n . A l s o t h e measurement o f the p r o p e r t i e s o f a SF e l e c t r o d e w i t h an e x t r e m e l y s m a l l l e a d i n g - o f f a r e a o f o n l y 0.0005 t o 0.0007 mm would be of i n t e r e s t . A few recommendations c o n c e r n t h e e x p e r i m e n t a l a p p a r a t u s . In o r d e r t o improve the measurement a c c u r a c y , t h e f o l l o w i n g p o i n t s s h o u l d be t a k e n i n t o c o n s i d e r a t i o n : • V a r i a b l e a m p l i t u d e o f t h e d i p o l e c u r r e n t I . F o r s m a l l r , t h e measured v o l t a g e s h o u l d not exceed c e r t a i n l i m i t s (see f o r example P l o n s e y , 1969) i n o r d e r t o s t a y out of n o n - l i n e a r e l e c t r o d e impedance e f f e c t s . • The d i p o l e c u r r e n t f r e q u e n c y used s h o u l d be c a r e f u l l y e v a l u a t e d f o r minimum s h u n t i n g w i t h o u t r u n n i n g t h e r i s k o f t o o s l o w l y c h a n g i n g a m p l i t u d e s , c a u s i n g n o n - l i n e a r e l e c t r o c h e m i c a l p r o c e s s e s . • V a r i a b l e and c a l i b r a t e d a m p l i f i e r g a i n . • E f f e c t i v e n o i s e f i l t e r i n g . a Temperature c o n t r o l o f the e l e c t r o l y t e . 112 In another s t e p , the f r e q u e n c y e f f e c t c o u l d be modeled i n an e l e c t r o l y t i c tank w i t h a moving d i p o l e . Then t h e s h u n t i n g c o u l d be measured as a f u n c t i o n o f f r e q u e n c y , where t h e problem of t h e g e o m e t r i c a l s i m i l a r i t y o f s h u n t i n g would s t i l l n o t be s o l v e d . F o r t h e l a t t e r , d i f f e r e n t e l e c t r o l y t e c o n c e n t r a t i o n s (which a f f e c t t h e r a t i o o f the b u l k r e s i s t i v i t y o f t h e e l e c t r o l y t e and t h e s p e c i f i c i n t e r f a c e impedance) would be o f i n t e r e s t . More s o p h i s t i c a t e d measurement t e c h n i q u e s w i t h computer a c q u i s i t i o n would make the d a t a h a n d l i n g much e a s i e r . Not o n l y c o u l d d i s p e r s i o n be t a k e n i n t o a c c o u n t b u t a l s o more f e a t u r e s o f t h e r e c o r d e d AP's c o u l d be e x t r a c t e d . Important a r e f o r example t h e t h r e e b a s i c e f f e c t s o f s h u n t i n g , w a l l e f f e c t and a v e r a g i n g as a f u n c t i o n o f the l e n g t h / t i m e z (most r e s u l t s o f t h o s e e f f e c t s were g i v e n as a f u n c t i o n o f r ) , i n o r d e r t o t h o r o u g h l y a s s e s s t h e shape d i s t o r t i o n s , n o t j u s t PTPA d e c r e a s e s o r i n c r e a s e s . 113 BIBLIOGRAPHY A d r i a n ED & Bronk DW (1929). D i s c h a r g e o f Impulses i n Motor Nerve F i b e r s . J P h y s i o l (Lond.) 67:119. A i d l e y DJ (1978). The P h y s i o l o g y o f E x c i t a b l e C e l l s . Cambridge U n i v e r s i t y P r e s s , Cambridge. Basmajian JV (1962). Muscles A l i v e : T h e i r F u n c t i o n s R e v e a l e d by EMG. W i l l i a m s & W i l k i n s Co, B a l t i m o r e , MD. Basmajian JV & Stecko G (1962). A New B i p o l a r E l e c t r o d e f o r E l e c t r o m y o g r a p h y . J A p p l P h y s i o l 17:849. B o c k r i s J O'M & Reddy AKM (1970). Modern E l e c t r o c h e m i s t r y . Plenum P r e s s , New York. Boyd DC, Lawrence PD & B r a t t y PJA (1978). On M o d e l i n g t h e S i n g l e Motor U n i t A c t i o n P o t e n t i a l . IEEE Trans Biomed Eng BME-25, No 3:236. B r a n d s t a t e r ME & Lambert EH (1973). Motor U n i t Anatomy (p 14 i n : New Dev e l o p -ments i n Electromyography and C l i n i c a l N e u r o p h y s i o l o g y , J E Desmedt e d ) . Ka r g e r , B a s e l , S w i t z . Brummer SB & Tu r n e r MJ (1977). E l e c t r o c h e m i c a l C o n s i d e r a t i o n s f o r S a f e E l e c -t r i c a l S t i m u l a t i o n o f t h e Nervous System w i t h P l a t i n u m E l e c t r o d e s . IEEE Trans Biomed Eng BME-27, No 7:59. B u c h t h a l F, G u l d C & R o s e n f a l c k P (1954). A c t i o n P o t e n t i a l Parameters i n Nor-mal Human Muscle and T h e i r Dependence on P h y s i c a l V a r i a b l e s . A c t a Phys Scand 32:200. (1957a). Volume C o n d u c t i o n o f t h e S p i k e o f t h e Motor U n i t P o t e n t i a l I n v e s t i g a t e d w i t h a New Type o f M u l t i e l e c t r o d e . A c t a Phys Scand 38:331. (1957b). M u l t i e l e c t r o d e Study o f t h e T e r r i t o r y o f a Motor U n i t . A c t a Phys Scand 39:83. B u c h t h a l F & R o s e n f a l c k P (1973). On t h e S t r u c t u r e o f Motor U n i t s (p 71 i n : New Developments i n El e c t r o m y o g r a p h y and C l i n i c a l N e u r o p h y s i o l o g y , J E Desmedt e d ) . Kar g e r , B a s e l , S w i t z . B u r k h a r d t D (1957). D i e U e b e r t r a g u n g s e i g e n s c h a f t e n e l e k t r o p h y s i o l o g i s c h e r Versuchsanordnungen. Z B i o l 109:297. C a r l s o n NR (1977). P h y s i o l o g y o f B e h a v i o r . A l l y n & Bacon, Inc, Boston, Mass. C h r i s t e n s e n E (1959). Topography o f T e r m i n a l Motor I n n e r v a t i o n i n S t r i a t e d Muscles From S t i l l - B o r n I n f a n t . Amer J Phys Med 38:65. 114 Cromwell L, W e i b e l l F J & P f e i f f e r EA (1980). B i o m e d i c a l I n s t r u m e n t a t i o n and Measurements. P r e n t i c e - H a l l , Inc, Englewood C l i f f s , NJ. DISA E l e k t r o m y o g r a p h i e - E l e k t r o d e n - H a n d b u c h . Skovlunde, Denmark 1976. Dymond AM (1976). C h a r a c t e r i s t i c s o f t h e M e t a l - T i s s u e I n t e r f a c e o f S t i m u l a -t i o n E l e c t r o d e s . IEEE Trans Biomed Eng BME-23, No 4:274. E k s t e d t J (1964). Human S i n g l e Muscle F i b e r A c t i o n P o t e n t i a l s . A c t a Phys Scand 61 Suppl 226:1-96. E k s t e d t J & S t a l b e r g E (1973). How t h e S i z e of t h e Needle E l e c t r o d e L e a d i n g -o f f S u r f a c e I n f l u e n c e s the Shape of the S i n g l e Muscle F i b e r A c t i o n P o t e n -t i a l i n E l e c t r o m y o g r a p h y . Comp Progr B i o m e d i c i n e 3:204. F e r r i s CD (1974). I n t r o d u c t i o n t o B i o e l e c t r o d e s . Plenum P r e s s , New York. F e r r i s CD & Stewart LR (1974). E l e c t r o d e - P r o d u c e d S i g n a l D i s t o r t i o n i n E l e c -t r o p h y s i o l o g i c a l R e c o r d i n g Systems. IEEE Trans Biomed Eng BME-23, No 4:318. F l e c k H (1962). A c t i o n P o t e n t i a l s From S i n g l e Motor U n i t s i n Human M u s c l e . A r c h Phys Med R e h a b i l 43:99. Gath I & S t a l b e r g E (1976). T e c h n i q u e s f o r Improving t h e S e l e c t i v i t y f o r EMG R e c o r d i n g s . IEEE Trans Biomed Eng BME-26, No 6:467. (1978). The C a l c u l a t e d R a d i a l D e c l i n e o f t h e E x t r a c e l l u l a r A c t i o n P o t e n t i a l Compared w i t h In S i t u Measurements i n the Human B r a c h i a l B i c e p s . E l e c t r o e n c e p h a l C l i n N e u r o p h y s i o l 44:547. Geddes LA (1972). E l e c t r o d e s and t h e Measurement o f B i o e l e c t r i c E v e n t s . John W i l e y & Sons, Inc, New York. George RE (1970). The Summation o f Muscle F i b e r A c t i o n P o t e n t i a l s . Med B i o l Eng 8:357. G l a s s t o n e S (1949). An I n t r o d u c t i o n t o E l e c t r o c h e m i s t r y . D van N o s t r a n d Co, Inc, P r i n c e t o n , NY. G r e a t b a t c h W e t a l (1969) . P o l a r i z a t i o n Phenomena R e l a t i n g t o P h y s i o l o g i c a l E l e c t r o d e s . Ann NY Acad S c i 167:722. Guld C, R o s e n f a l c k A & W i l l i s o n RG (1970). T e c h n i c a l F a c t o r s i n R e c o r d i n g E l e c t r i c a l A c t i v i t y o f Muscle and Nerve i n Man. E l e c t r o e n c e p h a l C l i n N e u r o p h y s i o l 28:399. 115 Helmholtz H (1853). Ueber e i n i g e Gesetze der V e r t h e i l u n g e l e k t r i s c h e r Strome i n k o r p e r l i c h e n L e i t e r n m i t Anwendung auf d i e t h i e r i s c h - e l e k t r i s c h e n V e r s u c h e . Ann P h y s i k u Chemie 89:211, 353. Hakannson CH (1956). C o n d u c t i o n V e l o c i t y and Amplitude o f the A c t i o n P o t e n t i a l as R e l a t e d t o C i r c u m f e r e n c e i n t h e I s o l a t e d F i b e r o f F r o g M u s c l e . A c t a Phys Scand 37:14. Hannerz J (1974). An E l e c t r o d e f o r R e c o r d i n g S i n g l e Motor U n i t A c t i v i t y D u r i n g S t r o n g Muscle C o n t r a c t i o n . E l e c t r o e n c e p h a l C l i n N e u r o p h y s i o l 37:179. J a s p e r HH, Johnson RT & Geddes LA (1945). The RCAMC E l e c t r o m y o g r a p h . Can Army Med Rept C6174. J a s p e r HH & B a l l e m G (1949). U n i p o l a r EMGs o f Normal and Denerva t e d Human Muscl e . J N e u r o p h y s i o l 12:231. Johnson EW ed (1980). P r a c t i c a l E l e c t r o m y o g r a p h y . W i l l i a m s & W i l k i n s Co, B a l t i m o r e , MD. L o r e n t e de N6 R (1947). A Study o f Nerve P h y s i o l o g y . S t u d i e s from t h e R o c k e f e l l e r I n s t i t u t e f o r M e d i c a l Research 132:394. L u n d e r v o l d A & L i C-L (1953). Motor U n i t s and F i b r i l l a t i o n P o t e n t i a l s as Recorded w i t h D i f f e r e n t K i n d s o f Needle E l e c t r o d e s . A c t a P s y c h i a t r Scand 28:201. Nastuk WL ed (1963). E l e c t r o p h y s i o l o g i c a l Methods, P a r t B (Volume V I from P h y s i c a l Techniques i n B i o l o g i c a l R e s e a r c h ) . Academic P r e s s , Inc, New York. P e t e r s e n I & K u g e l b e r g E (1949). D u r a t i o n and Form o f A c t i o n P o t e n t i a l i n t h e Normal Human Musc l e . J N e u r o l Neurosurg P s y c h i a t r y 12:124. P l o n s e y R (1969). B i o e l e c t r i c Phenomena. Mc G r a w - H i l l , New York. P o l l a k V (1971). The Waveshape o f A c t i o n P o t e n t i a l s Recorded w i t h D i f f e r e n t Types o f E l e c t r o m y o g r a p h i c N e e d l e s . Med B i o l Eng 9:657. (1974a). An E q u i v a l e n t Diagram f o r t h e I n t e r f a c e Impedance o f M e t a l Needle E l e c t r o d e s . Med B i o l Eng 12:454. (1974b). Computation o f t h e Impedance C h a r a c t e r i s t i c s o f M e t a l E l e c -t r o d e s f o r B i o l o g i c a l I n v e s t i g a t i o n s . Med B i o l Eng 12:460. (1974c). Impedance Measurements on M e t a l Needle E l e c t r o d e s . Med B i o l Eng 12:606. 116 R e i n e r S & Rogoff JB (1980). I n s t r u m e n t a t i o n ( i n : P r a c t i c a l E l e c t r o m y o g r a p h y , E Johnson e d ) . W i l l i a m s & W i l k i n s Co, B a l t i m o r e , MD. R o s e n f a l c k P (1957). Volume Conducted A c t i o n P o t e n t i a l s and T h e i r C o r r e l a t i o n t o the I n t r a c e l l u l a r P o t e n t i a l s . A c t a Phys Scand 42 Suppl 145:118. (1969). I n t r a - and E x t r a c e l l u l a r P o t e n t i a l F i e l d s o f A c t i v e Nerve and Muscle F i b e r s . A c t a Phys Scand Suppl 321:1-168. Schwan HP (1957). E l e c t r i c a l P r o p e r t i e s o f T i s s u e and C e l l S u s p e n s i o n s (p 147 i n : Advances i n B i o l o g i c a l and M e d i c a l P h y s i c s , Volume V, ed JH Lawrence e t a l ) . Academic P r e s s , Inc, New York. (1963). D e t e r m i n a t i o n of B i o l o g i c a l Impedances (p 323 i n : P h y s i c a l Techniques i n B i o l o g i c a l Research, V o l IV P a r t B, W Nastuk e d ) . Academic P r e s s , Inc, New York. (1968). E l e c t r o d e P o l a r i z a t i o n Impedance and Measurements i n B i o -l o g i c M a t e r i a l s . Ann NY Acad S c i 148:191. S t a l b e r g E (1980). Macro EMG, a New R e c o r d i n g T e c h n i q u e . J N e u r o l Neurosurg P s y c h i a t r y 43:475. S t a l b e r g E & A n t o n i L (1980). E l e c t r o p h y s i o l o g i c a l C r o s s S e c t i o n o f t h e Motor U n i t . J N e u r o l N e u r o s u r g P s y c h i a t r y 43:469. S t a l b e r g E & Gath I ( i n p r e s s ) . In S i t u Measurement of the I n n e r v a t i o n R a t i o o f Motor U n i t s i n Human M u s c l e s . IEEE Trans Biomed Eng. S t a l b e r g E & T r o n t e l j JV (1979). S i n g l e F i b e r E l e c t r o m y o g r a p h y . M i r v a i l l e P r e s s L t d , O l d Woking, S u r r e y UK. S t a l b e r g E, Schwartz MS, T h i e l e B & S c h i l l e r HH (1976). The Normal Motor U n i t i n Man. J N e u r o l S c i 27:291. S t r a t t o n JA (1941). E l e c t r o m a g n e t i c Theory. The Maple P r e s s Company, New York. S t r a u b W (1922). N a d e l e l e k t r o d e n B e i E l e k t r o k a r d i o g r a p h i e . K l i n Wochenschr 1:1638. T h i e l e B & Boehle A (1975). Number of S i n g l e Muscle F i b e r A c t i o n P o t e n t i a l s C o n t r i b u t i n g t o the Motor U n i t P o t e n t i a l . 5th I n t e r n a t i o n a l Congress of EMG, R o c h e s t e r , Minn, p 67. 117 Waring W (1974). O b s e r v i n g S i g n a l s From Nerve and Muscle (p 215 i n : B i o m e d i -c a l E l e c t r o n i c s Technique; Theory & P r a c t i c e , ed H M i l l e r e t a l ) . Academic P r e s s , Inc, New York. Weber E (1950). E l e c t r o m a g n e t i c F i e l d s . Theory and A p p l i c a t i o n s . John W i l e y & Sons, Inc, New York. Weinmann J & Mahler J (1964). An A n a l y s i s o f E l e c t r i c a l P r o p e r t i e s o f M e t a l E l e c t r o d e s . Med E l e c t r o n B i o l Eng 2:299. Wiechers DO, B l o o d JR & Stow RW (1979). EMG Needle E l e c t r o d e s : E l e c t r i c a l Impedance. Ar c h Phys Med R e h a b i l 60:364. 118 APPENDIX 119 Exact IZ5A 0 so: + 15V stab. Q sky X / ' fkt, 7 * /C ^3 5 6 5 2 N 4-920 OP, 2N4-126 OP,' 2N4-124-2N4-925 8.2 56 - / 5 V-Jt*lr. F I q u r e A . 1 . The c i r c u i t o f the c u r r e n t s o u r c e ( s e c t i o n 2 . 6 ) . 120 F i g u r e A . 2 . The c i r c u i t o f the a m p l i f i e r ( s e c t i o n 2 . 6 ) . 1 : 1 115 V ~ 60 Hz F 1 g u r e A . 3 . The s i g n a l f l o w c i r c u i t o f the c o m p l e t e e l e c t r i c a l a p p a r a t u s . Shown a r e the u n d e s l r e d c u r r e n t s In c a s e o f no I s o l a t e d power s u p p l y f o r the d i p o l e c u r r e n t s o u r c e . A l s o shown i s the common mode v o l t a g e Vcm a t t h e ' c o r e ' and ' c a n n u l a ' o f the CNE. 

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